Screen isotropic leaves and Simons' formula for null hypersurfaces
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We study the null hypersurfaces of a Lorentzian manifold through the rigging technique, which uses a convenient choice of a vector field in the ambient space to define a Riemannian metric. With this machinery at hand, we study the geometry of null hypersurfaces admitting screen isotropic leaves. In the second part of the paper, we establish a formula for the Laplacian of the null second fundamental form of a null hypersurface of a Lorentzian manifold with constant curvature. Based on this formula, we characterize null hypersurfaces for which the screen sectional curvature is non-negative. We also prove two de Rham-like decomposition theorems, showing that under suitable conditions, the null hypersurface has a triple product structure.
Abstract
We study the null hypersurfaces of a Lorentzian manifold through the rigging technique, which uses a convenient choice of a vector field in the ambient space to define a Riemannian metric. With this machinery at hand, we study the geometry of null hypersurfaces admitting screen isotropic leaves. In the second part of the paper, we establish a formula for the Laplacian of the null second fundamental form of a null hypersurface of a Lorentzian manifold with constant curvature. Based on this formula, we characterize null hypersurfaces for which the screen sectional curvature is non-negative. We also prove two de Rham-like decomposition theorems, showing that under suitable conditions, the null hypersurface has a triple product structure.
참고문헌 (12)
- C. Atindogbe, "Conformal screen on lightlike hypersurfaces", Int. J. Pure Appl. Math, 11, pp.421~442 (2006)
- C. Atindogbe, "Lightlike Einstein hypersurfaces in Lorentzian manifolds with constant curvature", Kodai Math. J, 29(1), pp.58~71 (2006)[DOI]
- C. Atindogbe, "Newton transformations on null hypersurfaces", Commun. Math, 23(1), pp.57~83 (2015)
- C. Atindogbe, "Normalized null hypersurfaces in Lorentzian manifolds admitting conformal vector fields", Differ. Geom. Dyn. Syst, 23, pp.1~17 (2021)
- K. L. Duggal, "Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications" (1996), Kluwer Academic
- K. L. Duggal, "Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics" (2010), Birkhauser Verlag
- M. Gulbahar, "Screen isotropic leaves on lightlike hypersurfaces of a Lorentzian manifold", Bull. Korean Math. Soc, 54(2), pp.429~442 (2017)[DOI]
- M. Gutierrez, "Induced Riemannian structures on null hypersurfaces", Math. Nachr, 289(10), pp.1219~1236 (2016)[DOI]
- S. W. Hawking, "The Large Scale Structure of Space-Time" (1973), Cambridge Univ. Press
- M. Navarro, "Null screen quasi-conformal hypersurfaces in semi-Riemannian manifolds and applications", Math. Nachr, 293(8), pp.1534~1553 (2020)[DOI]
- O. Palmas, "Null hypersurfaces with screen parallel shape operator", Mediterr. J. Math, 18(4), pp.133~ (2021)[DOI]
- J. Simons, "Minimal varieties in riemannian manifolds", Ann. of Math, 88, pp.62~105 (1968)[DOI]