메뉴 건너뛰기




Volumn 311, Issue 3, 1998, Pages 549-576

On Finsler geometry of submanifolds

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0032391784     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080050200     Document Type: Article
Times cited : (96)

References (57)
  • 2
    • 0012422875 scopus 로고
    • Sur les sous-varietes des varietes Finsleriennes
    • H. Akbar-Zadeh, Sur les sous-varietes des varietes Finsleriennes, C. R. Acad. Sci. Paris Ser. A-B 266 (1968), A146-A148.
    • (1968) C. R. Acad. Sci. Paris Ser. A-b , vol.266
    • Akbar-Zadeh, H.1
  • 3
    • 0039544287 scopus 로고
    • Über die minimalflächen in gefaserten Finsler-Räumen
    • W. Barthel, Über die Minimalflächen in gefaserten Finsler-Räumen, Ann. Mat. Pura Appl. 36 (1954), 159-190.
    • (1954) Ann. Mat. Pura Appl. , vol.36 , pp. 159-190
    • Barthel, W.1
  • 4
    • 0038951643 scopus 로고
    • Variationsprobleme der oberflächenfunktion in der Finslerschen geometrie
    • W. Barthel, Variationsprobleme der Oberflächenfunktion in der Finslerschen Geometrie, Math. Z. 62 (1955), 23-36.
    • (1955) Math. Z. , vol.62 , pp. 23-36
    • Barthel, W.1
  • 5
    • 0039544288 scopus 로고
    • Extremalprobleme in der Finslerschen inhaltsgeometrie
    • W. Barthel, Extremalprobleme in der Finslerschen Inhaltsgeometrie, Ann. Univ. Sarav 4 (1956), 171-183.
    • (1956) Ann. Univ. Sarav , vol.4 , pp. 171-183
    • Barthel, W.1
  • 6
    • 0001484238 scopus 로고
    • On a notable connection in Finsler geometry
    • D. Bao, S.S. Chern, On a notable connection in Finsler geometry, Houston J. Math. 19(1) (1993), 135-180.
    • (1993) Houston J. Math. , vol.19 , Issue.1 , pp. 135-180
    • Bao, D.1    Chern, S.S.2
  • 9
    • 0000418309 scopus 로고
    • Special immersions of Finsler spaces
    • A. Bejancu, Special immersions of Finsler spaces, Stud. Cerc. Mat. 39 (1987), 463-487.
    • (1987) Stud. Cerc. Mat. , vol.39 , pp. 463-487
    • Bejancu, A.1
  • 10
    • 0004659017 scopus 로고
    • Isometric embeddings of Finsler manifolds
    • D. Burago, S. Ivanov, Isometric embeddings of Finsler manifolds, (in Russian), Algebra i Analiz 5 (1993), 179-192; translated in St. Petersburg Math. J., 5 (1994), 159-169.
    • (1993) Algebra i Analiz , vol.5 , pp. 179-192
    • Burago, D.1    Ivanov, S.2
  • 11
    • 0000517421 scopus 로고
    • translated
    • D. Burago, S. Ivanov, Isometric embeddings of Finsler manifolds, (in Russian), Algebra i Analiz 5 (1993), 179-192; translated in St. Petersburg Math. J., 5 (1994), 159-169.
    • (1994) St. Petersburg Math. J. , vol.5 , pp. 159-169
  • 12
    • 0001628359 scopus 로고
    • Intrinsic area
    • H. Busemann, Intrinsic area, Ann. Math. 48(2) (1947), 234-267.
    • (1947) Ann. Math. , vol.48 , Issue.2 , pp. 234-267
    • Busemann, H.1
  • 16
    • 0001117362 scopus 로고
    • On the total curvature of immersed manifolds, I
    • B. Y. Chen, On the total curvature of immersed manifolds, I, Amer. J. Math. 93 (1971), 148-162.
    • (1971) Amer. J. Math. , vol.93 , pp. 148-162
    • Chen, B.Y.1
  • 17
    • 84959757411 scopus 로고
    • On a variational problem on hypersurfaces
    • B. Y. Chen, On a variational problem on hypersurfaces, J. London Math. Soc. (2) 6 (1973), 321-325.
    • (1973) J. London Math. Soc. (2) , vol.6 , pp. 321-325
    • Chen, B.Y.1
  • 18
    • 0040729656 scopus 로고    scopus 로고
    • A report on submanifolds of finite type
    • to appear
    • B. Y. Chen, A report on submanifolds of finite type, Soochow J. of Mathematics (to appear).
    • Soochow J. of Mathematics
    • Chen, B.Y.1
  • 19
    • 84972538046 scopus 로고
    • Inequalities between volume, center of mass, circumscribed radius, order, and mean curvature
    • B. Y. Chen, S. Jiang, Inequalities between volume, center of mass, circumscribed radius, order, and mean curvature, Bull. Soc. Math. Belg. (New Series) 2 (1975), 75-85.
    • (1975) Bull. Soc. Math. Belg. (New Series) , vol.2 , pp. 75-85
    • Chen, B.Y.1    Jiang, S.2
  • 20
    • 0003208121 scopus 로고
    • On the Euclidean connections in a Finsler space
    • or Selected Papers, vol. II, 107-111, Springer 1989
    • S.S. Chern, On the Euclidean connections in a Finsler space, Proc. National Acad. Sc. 29 (1943), 33-37; or Selected Papers, vol. II, 107-111, Springer 1989.
    • (1943) Proc. National Acad. Sc. , vol.29 , pp. 33-37
    • Chern, S.S.1
  • 21
    • 0001707043 scopus 로고
    • On Finsler geometry
    • S.S. Chern, On Finsler geometry, C. R. Acad. Sc. Paris 314 (1992), 757-761.
    • (1992) C. R. Acad. Sc. Paris , vol.314 , pp. 757-761
    • Chern, S.S.1
  • 22
    • 0040135749 scopus 로고
    • The induced curvature tensors of a subspace in a Finsler space
    • I. Comic, The induced curvature tensors of a subspace in a Finsler space, Tensor, N. S. 23 (1971), 21-34.
    • (1971) Tensor, N. S. , vol.23 , pp. 21-34
    • Comic, I.1
  • 23
    • 0040729655 scopus 로고
    • The intrinsic curvature tensors of a subspace in a Finsler space
    • I. Comic, The intrinsic curvature tensors of a subspace in a Finsler space, Tensor, N. S. 24 (1972), 19-28.
    • (1972) Tensor, N. S. , vol.24 , pp. 19-28
    • Comic, I.1
  • 24
    • 0040135748 scopus 로고
    • Induced and intrinsic curvature tensors of a subspace in the Finsler space
    • I. Comic, Induced and intrinsic curvature tensors of a subspace in the Finsler space, Publications de L'Institut Mathématiane 23 (37) (1978), 67-74.
    • (1978) Publications de L'Institut Mathématiane , vol.23 , Issue.37 , pp. 67-74
    • Comic, I.1
  • 25
    • 0040729639 scopus 로고
    • Curves in subspaces of recurrent Finsler spaces
    • I. Comic, Curves in subspaces of recurrent Finsler spaces, Note de Matematica IX (1989), 29-64.
    • (1989) Note de Matematica , vol.9 , pp. 29-64
    • Comic, I.1
  • 26
    • 0003316659 scopus 로고
    • Submanifolds and isometric immersions
    • Publish or Perish, Inc., Houston, Texas
    • M. Dajczer, Submanifolds and isometric immersions, Mathematics Lecture Series, no. 13, Publish or Perish, Inc., Houston, Texas, 1990.
    • (1990) Mathematics Lecture Series , vol.13
    • Dajczer, M.1
  • 27
    • 84960583771 scopus 로고
    • Subspaces of a Finsler space
    • E. T. Davies, Subspaces of a Finsler space, Proc. London Math. Soc. 49 (1947), 19-39
    • (1947) Proc. London Math. Soc. , vol.49 , pp. 19-39
    • Davies, E.T.1
  • 30
    • 84956267209 scopus 로고
    • Filling Riemannian manifolds
    • M. Gromov, Filling Riemannian manifolds, J. Diff. Geom. 18 (1983), 1-147
    • (1983) J. Diff. Geom. , vol.18 , pp. 1-147
    • Gromov, M.1
  • 31
    • 84967517634 scopus 로고
    • Imbedding of a Finsler manifold in a Minkowski space
    • C. H. Gu, Imbedding of a Finsler manifold in a Minkowski space, (in Chinese), Acta. Math. Sinica 7 (1957), 215-232
    • (1957) Acta. Math. Sinica , vol.7 , pp. 215-232
    • Gu, C.H.1
  • 32
    • 0040729652 scopus 로고
    • Imbeddings of Finsler manifolds in a Minkowski space
    • G. H. Gu, Imbeddings of Finsler manifolds in a Minkowski space, (in Chinese), Acta. Math. Sinica 8 (1958), 282-285
    • (1958) Acta. Math. Sinica , vol.8 , pp. 282-285
    • Gu, G.H.1
  • 33
    • 0038951637 scopus 로고
    • Sulle superficie totalmente geodetiche negli spazi di finsler
    • M. Haimovici, Sulle superficie totalmente geodetiche negli spazi di Finsler, Atti Accad. Naz. Lincei 27 (6) (1938), 633-641
    • (1938) Atti Accad. Naz. Lincei , vol.27 , Issue.6 , pp. 633-641
    • Haimovici, M.1
  • 35
    • 0038030298 scopus 로고
    • Über die einbetting eines Finslerschen Rammes in einan Minkowskischen Raum
    • R. S. Ingarden, Über die Einbetting eines Finslerschen Rammes in einan Minkowskischen Raum, Bull. Acad. Polon. Sci. III 2 (1954), 305-308
    • (1954) Bull. Acad. Polon. Sci. III , vol.2 , pp. 305-308
    • Ingarden, R.S.1
  • 36
    • 0040729649 scopus 로고
    • On the theory of subspace in a Finsler space
    • S. Kikuchi, On the theory of subspace in a Finsler space, Tensor, N. S. 2 (1952), 67-79
    • (1952) Tensor, N. S. , vol.2 , pp. 67-79
    • Kikuchi, S.1
  • 38
    • 0000115616 scopus 로고
    • The induced and intrinsic Finsler connections of a hypersurface and Finslerian projective geometry
    • M. Matsumoto, The induced and intrinsic Finsler connections of a hypersurface and Finslerian projective geometry, J. Math. Kyoto Univ. 25 (1985), 107-144
    • (1985) J. Math. Kyoto Univ. , vol.25 , pp. 107-144
    • Matsumoto, M.1
  • 39
    • 0010390349 scopus 로고
    • Theory of Y -extremal and minimal hypersurfaces in a Finsler space
    • M. Matsumoto, Theory of Y -extremal and minimal hypersurfaces in a Finsler space, J. Math. Kyoto Univ. 26 (1986), 647-665
    • (1986) J. Math. Kyoto Univ. , vol.26 , pp. 647-665
    • Matsumoto, M.1
  • 41
    • 0002702476 scopus 로고
    • The imbedding problem for Riemannian manifolds
    • J. Nash, The imbedding problem for Riemannian manifolds, Ann. Math. 73 (1957), 20-37
    • (1957) Ann. Math. , vol.73 , pp. 20-37
    • Nash, J.1
  • 42
    • 26744464973 scopus 로고
    • Eine neue charakterisierung Finslerscher Räume skalarer und konstanter krümmung und projective-ebene Räume
    • A. Rapcsák, Eine neue Charakterisierung Finslerscher Räume skalarer und konstanter krümmung und projective-ebene Räume, Acta Math. Acad. Sci. Hunger. 8 (1975), 1-18
    • (1975) Acta Math. Acad. Sci. Hunger. , vol.8 , pp. 1-18
    • Rapcsák, A.1
  • 44
    • 0040890295 scopus 로고
    • A divergence theorem for Finsler metrics
    • H. Rund, A divergence theorem for Finsler metrics, Monatsh. Math. 79 (1975), 233-252
    • (1975) Monatsh. Math. , vol.79 , pp. 233-252
    • Rund, H.1
  • 45
    • 0038951631 scopus 로고
    • Über die parallelverschiebung in Finslerschen Räumen
    • H. Rund, Über die parallelverschiebung in Finslerschen Räumen, Math. Z. 54 (1951), 115-128
    • (1951) Math. Z. , vol.54 , pp. 115-128
    • Rund, H.1
  • 46
    • 0038951635 scopus 로고
    • The theory of subspaces of a Finsler space. I
    • H. Rund, The theory of subspaces of a Finsler space. I, Math. Z. 56 (1952), 363-375
    • (1952) Math. Z. , vol.56 , pp. 363-375
    • Rund, H.1
  • 47
    • 0040729643 scopus 로고
    • The theory of subspaces of a Finsler space. II
    • H. Rund, The theory of subspaces of a Finsler space. II, Math. Z. 57 (1953), 193-210
    • (1953) Math. Z. , vol.57 , pp. 193-210
    • Rund, H.1
  • 48
    • 0038951632 scopus 로고
    • On the total curvature of immersions and minimal submanifolds of spheres
    • G. Rotondaro, On the total curvature of immersions and minimal submanifolds of spheres, Comment. Math. Univ. Carolina 34 (1993), 549-563
    • (1993) Comment. Math. Univ. Carolina , vol.34 , pp. 549-563
    • Rotondaro, G.1
  • 50
    • 0031586115 scopus 로고    scopus 로고
    • Volume comparison and its applications in Riemann-Finsler geometry
    • Z. Shen, Volume comparison and its applications in Riemann-Finsler geometry, Advances in Math., 128 (1997), 306-328.
    • (1997) Advances in Math. , vol.128 , pp. 306-328
    • Shen, Z.1
  • 51
    • 0000889923 scopus 로고
    • On a connection in Finsler geometry
    • Z. Shen, On a connection in Finsler geometry, Houston J. Math. 20 (1994), 591-602
    • (1994) Houston J. Math. , vol.20 , pp. 591-602
    • Shen, Z.1
  • 53
    • 0038951634 scopus 로고
    • Die krümmung der eichfläche des Minkowskischen Raumes und die geometrische deutung des einen krümmungs-tensors des Finslerschen Raumes
    • O. Varga, Die Krümmung der Eichfläche des Minkowskischen Raumes und die geometrische Deutung des einen Krümmungs-tensors des Finslerschen Raumes, Abh. Math. Sem. Univ. Hamburg 20 (1955), 41-51
    • (1955) Abh. Math. Sem. Univ. Hamburg , vol.20 , pp. 41-51
    • Varga, O.1
  • 56
    • 0039544278 scopus 로고
    • Untersuchungen über Finslerschen Räume
    • J. M. Wegener, Untersuchungen über Finslerschen Räume, Lotos 84 (1936), 4-7
    • (1936) Lotos , vol.84 , pp. 4-7
    • Wegener, J.M.1
  • 57
    • 0040729648 scopus 로고
    • Hyperflächen in Finslerschen Räumen als transversalflächen einer schar von extremalen
    • J. M. Wegener, Hyperflächen in Finslerschen Räumen als Transversalflächen einer Schar von Extremalen, Mh. Math. Phys. 44 (1936), 115-130.
    • (1936) Mh. Math. Phys. , vol.44 , pp. 115-130
    • Wegener, J.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.