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Volumn 34, Issue 2, 2003, Pages 303-331

Harmonic mean curvature lines on surfaces immersed in ℝ3

Author keywords

Harmonic mean curvature cycle; Harmonic mean curvature lines; Parabolic point; Umbilic point

Indexed keywords


EID: 0141683970     PISSN: 16787544     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00574-003-0015-2     Document Type: Article
Times cited : (15)

References (33)
  • 2
    • 0002564801 scopus 로고
    • Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature
    • Proc. Steklov Institute of Mathematics
    • D. V. Anosov, Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature, Proc. Steklov Institute of Mathematics, Amer. Math. Soc. Transl. 90 (1967) and (1969).
    • (1967) Amer. Math. Soc. Transl. , vol.90
    • Anosov, D.V.1
  • 4
    • 0003649602 scopus 로고
    • Springer-Verlag, Berlin
    • M. Berger, Geometry I, Springer-Verlag, Berlin, 1987.
    • (1987) Geometry I
    • Berger, M.1
  • 6
    • 84976161935 scopus 로고
    • On binary differential equations and umbilic points
    • B. Bruce and D. Fidal, On binary differential equations and umbilic points, Proc. Royal Soc. Edinburgh 111A (1989), 147-168.
    • (1989) Proc. Royal Soc. Edinburgh , vol.111 A , pp. 147-168
    • Bruce, B.1    Fidal, D.2
  • 7
    • 0000902530 scopus 로고
    • On binary differential equations
    • B. Bruce and F. Tari, On binary differential equations, Nonlinearity 8 (1995), 255-271.
    • (1995) Nonlinearity , vol.8 , pp. 255-271
    • Bruce, B.1    Tari, F.2
  • 8
    • 0141710987 scopus 로고    scopus 로고
    • Dupin indicatrices, families of curve congruences and the zero curves
    • W. Bruce and F. Tari, Dupin indicatrices, families of curve congruences and the zero curves, Notas de Matemática do ICMC-USP, 143 (2002), 1-31.
    • (2002) Notas de Matemática do ICMC-USP , vol.143 , pp. 1-31
    • Bruce, W.1    Tari, F.2
  • 10
    • 0004032132 scopus 로고
    • Sur la forme des lignes de courbure dans la voisinage d'un ombilic, Note 07, Paris: Gauthier Villars
    • G. Darboux, Leçons sur la Théorie des Surfaces, vol. IV. Sur la forme des lignes de courbure dans la voisinage d'un ombilic, Note 07, Paris: Gauthier Villars, 1896.
    • (1896) Leçons sur la Théorie des Surfaces , vol.4
    • Darboux, G.1
  • 11
    • 0141684691 scopus 로고
    • Qualitative Control Theory
    • Providence, R.I, Amer. Math. Soc.
    • A.A. Davydov, Qualitative Control Theory. Translations of Math. Monographs, 142, Providence, R.I, Amer. Math. Soc., 1994.
    • (1994) Translations of Math. Monographs , vol.142
    • Davydov, A.A.1
  • 13
    • 0042998886 scopus 로고    scopus 로고
    • Structural stability of parabolic points and periodic asymptotic lines
    • R. Garcia and J. Sotomayor, Structural stability of parabolic points and periodic asymptotic lines, Matemática Contemporânea, 12 (1997), 83-102.
    • (1997) Matemática Contemporânea , vol.12 , pp. 83-102
    • Garcia, R.1    Sotomayor, J.2
  • 18
    • 84966199279 scopus 로고
    • Positive quadratic differential forms and foliations with singularities on surfaces
    • V. Guíñez, Positive quadratic differential forms and foliations with singularities on surfaces, Trans. Amer. Math. Soc. 309(2): (1988), 477-502.
    • (1988) Trans. Amer. Math. Soc. , vol.309 , Issue.2 , pp. 477-502
    • Guíñez, V.1
  • 19
    • 0000216699 scopus 로고
    • Structural Stable Configurations of Lines of Principal Curvature
    • C. Gutierrez and J. Sotomayor, Structural Stable Configurations of Lines of Principal Curvature, Asterisque 98-99 (1982), 185-215.
    • (1982) Asterisque , vol.98-99 , pp. 185-215
    • Gutierrez, C.1    Sotomayor, J.2
  • 20
    • 0002582665 scopus 로고
    • An Approximation Theorem for Immersions with Structurally Stable Configurations of Lines of Principal Curvature
    • C. Gutierrez and J. Sotomayor, An Approximation Theorem for Immersions with Structurally Stable Configurations of Lines of Principal Curvature, Lect. Notes in Math. 1007 (1983).
    • (1983) Lect. Notes in Math. , vol.1007
    • Gutierrez, C.1    Sotomayor, J.2
  • 21
    • 0141710986 scopus 로고
    • Lines of Curvature and Umbilic Points on Surfaces
    • Rio de Janeiro, IMPA
    • th Brazilian Math. Colloquium, Rio de Janeiro, IMPA, 1991. Reprinted as Structurally Stable Configurations of Lines of Curvature and Umbilic Points on Surfaces, Lima, Monografias del IMCA, 1998.
    • (1991) th Brazilian Math. Colloquium
    • Gutierrez, C.1    Sotomayor, J.2
  • 22
    • 0141710985 scopus 로고    scopus 로고
    • Structurally Stable Configurations of Lines of Curvature and Umbilic Points on Surfaces, Lima
    • th Brazilian Math. Colloquium, Rio de Janeiro, IMPA, 1991. Reprinted as Structurally Stable Configurations of Lines of Curvature and Umbilic Points on Surfaces, Lima, Monografias del IMCA, 1998.
    • (1998) Monografias del IMCA
  • 23
    • 0001139914 scopus 로고    scopus 로고
    • Lines of Curvature, Umbilical Points and Carathéodory Conjecture
    • C. Gutierrez and J. Sotomayor, Lines of Curvature, Umbilical Points and Carathéodory Conjecture, Resenhas IME-USP, 03 (1998), 291-322.
    • (1998) Resenhas IME-USP , vol.3 , pp. 291-322
    • Gutierrez, C.1    Sotomayor, J.2
  • 25
    • 0002426142 scopus 로고
    • La décomposition dynamique et la differentiabilité des feiulletages des surfaces
    • G. Levitt, La décomposition dynamique et la differentiabilité des feiulletages des surfaces, Ann. Inst. Fourier, 37(3): (1987), 85-116.
    • (1987) Ann. Inst. Fourier , vol.37 , Issue.3 , pp. 85-116
    • Levitt, G.1
  • 27
    • 0141822235 scopus 로고
    • Sur un double systéme de lignes d'une surface
    • R. Occhipinti, Sur un double systéme de lignes d'une surface. L'enseignement mathématique, (1914), 38-44.
    • (1914) L'enseignement Mathématique , pp. 38-44
    • Occhipinti, R.1
  • 28
    • 0141599260 scopus 로고
    • On the T-System on a Surface
    • K. Ogura, On the T-System on a Surface, Tohoku Math. Journal, 09 (1916), 87-101.
    • (1916) Tohoku Math. Journal , vol.9 , pp. 87-101
    • Ogura, K.1
  • 29
    • 50549184010 scopus 로고
    • Structural Stability on two-dimensional manifolds
    • M. Peixoto, Structural Stability on two-dimensional manifolds, Topology 1 (1962), 101-120.
    • (1962) Topology , vol.1 , pp. 101-120
    • Peixoto, M.1
  • 30
    • 0141710984 scopus 로고
    • Sur le réseau diagonal conjugé
    • M. L. Raffy, Sur le réseau diagonal conjugé, Bull, de la Soc. Math. France 30 (1902), 226-233.
    • (1902) Bull, de la Soc. Math. France , vol.30 , pp. 226-233
    • Raffy, M.L.1
  • 31
    • 0000069710 scopus 로고
    • Labyrinths on the disk and surfaces
    • H. Rosenberg, Labyrinths on the disk and surfaces, Ann. of Math. 117 (1983), 1-33.
    • (1983) Ann. of Math. , vol.117 , pp. 1-33
    • Rosenberg, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.