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SCREEN CONFORMAL EINSTEIN LIGHTLIKE HYPERSURFACES OF A LORENTZIAN SPACE FORM

진대호
대한수학회 (The Korean Mathematical Society)|2010.04|대한수학회논문집 (Communications of the KMS)|제25권 제2호|pp. 225-234

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키워드

screen conformalEinstein lightlike hypersurfacesLorentzian space forms
주제분류수학

초록

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-vanishing smooth function.

Abstract

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-vanishing smooth function.

참고문헌 (9)

  1. C. Atindogbe, "Conformal screen on lightlike hypersurfaces", Int. J. Pure Appl. Math., 11(4), pp.421~442 (2004)
  2. C. Atindogbe, "Lightlike Einstein hypersurfaces in Lorentzian manifolds with constant curvature", Kodai Math. J., 29(1), pp.58~71 (2006)
  3. K. L. Duggal, "Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications" (1996), Kluwer Acad. Publishers
  4. K. L. Duggal, "Null curves and Hypersurfaces of Semi-Riemannian Manifolds" (2007), World Scientific Publishing Co. Pte. Ltd.
  5. K. L. Duggal, "A Classification of Einstein lightlike hypersurfaces of a Lorentzian space form", J. Geom. Phys.
  6. 진대호, "SCREEN CONFORMAL LIGHTLIKE HYPERSURFACES OF A SEMI-RIEMANNIAN SPACE FORM", 순수 및 응용수학, 16(3), pp.271~276 (2009), 한국수학교육학회
  7. D. N. Kupeli, "Singular Semi-Riemannian Geometry, Mathematics and Its Applications, vol. 366" (1996), Kluwer Acad. Publishers
  8. G. de Rham, "Sur la reductibilit`e d’un espace de Riemann", Comment. Math. Helv., 26, pp.328~344 (1952)
  9. P. J. Ryan, "Homogeneity and some curvature conditions for hypersurfaces", Tohoku Math. J., 21, pp.363~388 (1969)

관련 논문AI추천

Einstein lightlike hypersurfaces of a Lorentzian space form with a semi-symmetric metric connection진대호대한수학회 · 대한수학회논문집2013 · 제28권 제1호EINSTEIN HALF LIGHTLIKE SUBMANIFOLDS WITH SPECIAL CONFORMALITIES송대진, 진대호대한수학회 · 대한수학회보2012 · 제49권 제6호Einstein lightlike hypersurfaces of a Lorentz space form with a semi-symmetric non-metric connection진대호대한수학회 · 대한수학회보2013 · 제50권 제4호SCREEN CONFORMAL LIGHTLIKE HYPERSURFACES OF A SEMI-RIEMANNIAN SPACE FORM진대호한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제3호SCREEN CONFORMAL LIGHTLIKE REAL HYPERSURFACES OF AN INDEFINITE COMPLEX SPACE FORM진대호대한수학회 · 대한수학회보2010 · 제47권 제2호A Characterization Theorem for Lightlike Hypersurfaces of Semi-Riemannian Manifolds of Quasi-Constant Curvatures진대호영남수학회 · East Asian Mathematical Journal2014 · 제30권 제1호

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