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THE AXIOM OF INDEFINITE SURFACES IN SEMI-RIEMANNIAN MANIFOLDS

진대호|이재원
한국수학교육학회|2011.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제18권 제4호|pp. 353-359

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참고문헌

키워드

lightlike submanifoldstotally umbilicalindefinite `-surfaces.
주제분류수학

초록

In this paper, we characterize a semi-Riemannian manifolds satisfies the axiom of indefinite surfaces. We obtain the following result: If a semi-Riemannian manifold satisfies the axiom of indefinite surfaces, then it is a real space form.

Abstract

In this paper, we characterize a semi-Riemannian manifolds satisfies the axiom of indefinite surfaces. We obtain the following result: If a semi-Riemannian manifold satisfies the axiom of indefinite surfaces, then it is a real space form.

참고문헌 (7)

  1. Cartan, E, "Lecons sur la geometrie des espaces de Riemann" (1946), Gauthiers-Villars
  2. Duggal, K.L, "Lightlike Submanifolds of Semi -Riemannian Manifolds and Applications" (1996), Kluwer Acad. Publishers
  3. Duggal, K.L, "Totally umbilical lightlike submanifolds", Kodai Math. J, 26, pp.49~68 (2003)
  4. Graves, L., "On sectional curvature of indefinite metric I", Math. Ann, 232, pp.267~272 (1978)
  5. Kumar, R., "The axiom of spheres in semi-Riemannian geom- etry with lightlike submanifolds", Kodai Math. J, 32, pp.52~58 (2009)
  6. Leung, D.S., "The axiom of spheres in Riemannian geometry", J. Differential Geometry, 5, pp.487~489 (1971)
  7. O'Neill, B, "Semi -Riemannian Geometry with Applications to Relativity" (1983), Academic Press

관련 논문AI추천

Singular Theorems for Lightlike Submanifolds in a Semi-Riemannian Space Form진대호영남수학회 · East Asian Mathematical Journal2014 · 제30권 제3호On the Geometry of Lightlike Submanifolds강태호경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2011 · 제51권 제2호A Characterization Theorem for Lightlike Hypersurfaces of Semi-Riemannian Manifolds of Quasi-Constant Curvatures진대호영남수학회 · East Asian Mathematical Journal2014 · 제30권 제1호SEMI-RIEMANNIAN SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTIONAhmet Yucesan, Erol Yasar대한수학회 · 대한수학회논문집2012 · 제27권 제4호SCREEN CONFORMAL LIGHTLIKE REAL HYPERSURFACES OF AN INDEFINITE COMPLEX SPACE FORM진대호대한수학회 · 대한수학회보2010 · 제47권 제2호A semi-Riemannian manifold of quasi-constant curvature admits some half lightlike submanifolds진대호대한수학회 · 대한수학회보2013 · 제50권 제3호

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