메뉴 건너뛰기




Volumn 73, Issue 1, 1998, Pages 39-56

Volume Comparison Theorems for Lorentzian Manifolds

Author keywords

Geodesic wedges; Raychaudhuri equation; Riccati equation; Volume comparison

Indexed keywords


EID: 0001776694     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1005096913126     Document Type: Article
Times cited : (23)

References (28)
  • 1
    • 0002032399 scopus 로고    scopus 로고
    • Comparison and rigidity theorems in semi-Riemannian geometry
    • to appear in
    • Andersson, L. and Howard, R.: Comparison and rigidity theorems in semi-Riemannian geometry, to appear in Comm. Anal. Geom.
    • Comm. Anal. Geom.
    • Andersson, L.1    Howard, R.2
  • 2
    • 21344466444 scopus 로고    scopus 로고
    • Boundary and lens rigidity of Lorentzian surfaces
    • Andersson, L., Dahl, M. and Howard, R.: Boundary and lens rigidity of Lorentzian surfaces, Trans. Amer. Math. Soc. 348 (1996), 2307-2329.
    • (1996) Trans. Amer. Math. Soc. , vol.348 , pp. 2307-2329
    • Andersson, L.1    Dahl, M.2    Howard, R.3
  • 3
  • 5
    • 0000857099 scopus 로고
    • A relation between volume, mean curvature, and diameter
    • Bishop, R.: A relation between volume, mean curvature, and diameter, Notices Amer. Math. Soc. 10 (1963), 364.
    • (1963) Notices Amer. Math. Soc. , vol.10 , pp. 364
    • Bishop, R.1
  • 6
    • 0013480391 scopus 로고
    • Geometry of Manifolds
    • Academic Press, New York
    • Bishop, R. and Crittenden, R.: Geometry of Manifolds, Pure Appl. Math. 15, Academic Press, New York, 1964.
    • (1964) Pure Appl. Math. , vol.15
    • Bishop, R.1    Crittenden, R.2
  • 8
    • 0001409531 scopus 로고
    • Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds
    • Chicone, C. and Ehrlich, P.: Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds, Manuscripta Math. 31 (1980), 297-316.
    • (1980) Manuscripta Math. , vol.31 , pp. 297-316
    • Chicone, C.1    Ehrlich, P.2
  • 9
    • 0005139356 scopus 로고
    • From the Riccati Inequality to the Raychaudhuri Equation
    • Amer. Math. Soc., Providence
    • Ehrlich, P. and Kim, S.-B.: From the Riccati Inequality to the Raychaudhuri Equation, Contemp. Math. 170, Amer. Math. Soc., Providence, 1994, pp. 65-78.
    • (1994) Contemp. Math. , vol.170 , pp. 65-78
    • Ehrlich, P.1    Kim, S.-B.2
  • 10
    • 0041551610 scopus 로고
    • Stabilitätsverhalten des Geodätischen Flusses Riemannscher Mannigfaltigkeiten
    • Eschenburg, J.-H.: Stabilitätsverhalten des Geodätischen Flusses Riemannscher Mannigfaltigkeiten, Bonner Mathematische Schriften 87 (1976).
    • (1976) Bonner Mathematische Schriften , pp. 87
    • Eschenburg, J.-H.1
  • 11
    • 0000027620 scopus 로고
    • Comparison theorems and hypersurfaces
    • Eschenburg, J.-H.: Comparison theorems and hypersurfaces, Manuscripta Math. 59 (1987), 295-323.
    • (1987) Manuscripta Math. , vol.59 , pp. 295-323
    • Eschenburg, J.-H.1
  • 12
    • 51249171351 scopus 로고
    • Comparison theory for Riccati equations
    • Eschenburg, J.-H. and Heintze, E.: Comparison theory for Riccati equations, Manuscripta Math. 68 (1990), 209-214.
    • (1990) Manuscripta Math. , vol.68 , pp. 209-214
    • Eschenburg, J.-H.1    Heintze, E.2
  • 13
    • 0010193339 scopus 로고
    • Growth of Jacobi fields and divergence of geodesics
    • Eschenburg, J.-H. and O'Sullivan, J.: Growth of Jacobi fields and divergence of geodesics, Math. Z. 150 (1976), 221-237.
    • (1976) Math. Z. , vol.150 , pp. 221-237
    • Eschenburg, J.-H.1    O'Sullivan, J.2
  • 14
    • 0011682799 scopus 로고
    • Jacobi tensors and Ricci curvature
    • Eschenburg, J.-H. and O'Sullivan, J.: Jacobi tensors and Ricci curvature, Math. Ann. 252 (1980), 1-26.
    • (1980) Math. Ann. , vol.252 , pp. 1-26
    • Eschenburg, J.-H.1    O'Sullivan, J.2
  • 15
    • 84981915246 scopus 로고
    • Über Volumendefekte und Krummung in Riemannsche Mannigfältigkeiten mit Anwendungen in der Relativitätstheorie
    • Gackstatter, F. and Gackstatter, B.: Über Volumendefekte und Krummung in Riemannsche Mannigfältigkeiten mit Anwendungen in der Relativitätstheorie, Annal. Phys. 41 (1984), 35-44.
    • (1984) Annal. Phys. , vol.41 , pp. 35-44
    • Gackstatter, F.1    Gackstatter, B.2
  • 18
    • 0003372262 scopus 로고
    • Metric differential geometry
    • V. Hansen (ed.), Nordic Summer School, Lyngby 1985, Springer-Verlag, New York
    • Grove, K.: Metric differential geometry, In: V. Hansen (ed.), Nordic Summer School, Lyngby 1985, Lecture Notes in Math. 1263, Springer-Verlag, New York, 1987, pp. 171-227.
    • (1987) Lecture Notes in Math. , vol.1263 , pp. 171-227
    • Grove, K.1
  • 19
    • 0001210884 scopus 로고
    • A triangle comparison theorem for Lorentz manifolds
    • Harris, S.: A triangle comparison theorem for Lorentz manifolds, Indiana Math. J. 31 (1982), 289-308.
    • (1982) Indiana Math. J. , vol.31 , pp. 289-308
    • Harris, S.1
  • 21
    • 0001161574 scopus 로고
    • Riemannian comparison constructions
    • S. S. Chern, (ed.), Global Differential Geometry, Math. Assoc. Amer., Washington
    • Karcher, H.: Riemannian comparison constructions, in: S. S. Chern, (ed.), Global Differential Geometry, MAA Stud. Math. 27, Math. Assoc. Amer., Washington, 1989, pp. 170-222.
    • (1989) MAA Stud. Math. , vol.27 , pp. 170-222
    • Karcher, H.1
  • 22
    • 0042553729 scopus 로고
    • On existence and comparison of conjugate points in Riemannian and Lorentzian geometry
    • Kupeli, D. N.: On existence and comparison of conjugate points in Riemannian and Lorentzian geometry, Math. Ann. 276 (1986) 67-79.
    • (1986) Math. Ann. , vol.276 , pp. 67-79
    • Kupeli, D.N.1
  • 23
    • 0003311802 scopus 로고
    • Semi-Riemannian Geometry with Applications to Relativity
    • Academic Press, New York
    • O'Neill, B.: Semi-Riemannian Geometry with Applications to Relativity, Pure Appl. Math., Academic Press, New York, 1983.
    • (1983) Pure Appl. Math.
    • O'Neill, B.1
  • 24
    • 0041551608 scopus 로고
    • The volume problem for pseudo-Riemannian manifolds
    • Schimming, R. and Matel-Kaminska, D.: The volume problem for pseudo-Riemannian manifolds, Z. Anal. Anwendungen 9 (1990), 3-14.
    • (1990) Z. Anal. Anwendungen , vol.9 , pp. 3-14
    • Schimming, R.1    Matel-Kaminska, D.2
  • 25
    • 0013076097 scopus 로고
    • Singularities and causality violation
    • Tipler, F.: Singularities and causality violation, Ann. of Phys. 108 (1977), 1-36.
    • (1977) Ann. of Phys. , vol.108 , pp. 1-36
    • Tipler, F.1
  • 26
    • 0000458633 scopus 로고
    • General Relativity and conjugate ordinary differential equations
    • Tipler, F.: General Relativity and conjugate ordinary differential equations, J. Differential Equations 30 (1978), 165-174.
    • (1978) J. Differential Equations , vol.30 , pp. 165-174
    • Tipler, F.1
  • 27
    • 21844490979 scopus 로고
    • Causality relations on a class of space-times
    • Walschap, G.: Causality relations on a class of space-times, General Relativity Gravitation 27 (1995), 721-733.
    • (1995) General Relativity Gravitation , vol.27 , pp. 721-733
    • Walschap, G.1
  • 28
    • 0011910262 scopus 로고
    • A volume comparison theorem for manifolds with asymptotically nonnegative curvature and its applications
    • Zhu, S.-H.: A volume comparison theorem for manifolds with asymptotically nonnegative curvature and its applications, Amer. J. Math. 116 (1994), 669-682.
    • (1994) Amer. J. Math. , vol.116 , pp. 669-682
    • Zhu, S.-H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.