منابع مشابه
Umbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms
We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...
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Let (M, g) be a complete three dimensional Riemannian manifold with boundary ∂M . Given smooth functions K(x) > 0 and c(x) defined on M and ∂M , respectively, it is natural to ask whether there exist metrics conformal to g so that under these new metrics, K is the scalar curvature and c is the boundary mean curvature. All such metrics can be described by a prescribing curvature equation with a ...
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متن کاملumbilicity of (space-like) submanifolds of pseudo-riemannian space forms
we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...
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We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1934
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1934-05804-x