Results 1 to 10 of about 327 (148)
Global pinching theorems of submanifolds in spheres [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 Let M be a compact embedded submanifold with parallel mean curvature vector and positive Ricci curvature in the unit sphere S n+p(n≥2 ,p≥1). By using the Sobolev inequalities of P.
Kairen Cai
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On complete trapped submanifolds in globally hyperbolic spacetimes
Journal of Physics A: Mathematical and Theoretical, 2023 Abstract The aim of this manuscript is to obtain rigidity and non-existence results for parabolic spacelike submanifolds with causal mean curvature vector field in orthogonally splitted spacetimes, and in particular, in globally hyperbolic spacetimes.
Alma L. Albujer +2 more
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Semi-global extension of maximally complex submanifolds [PDF]
Bulletin of the Australian Mathematical Society, 2006 AbstractLet A be a domain of the boundary of a (weakly) pseudoconvex domain Ω of ℂn and M a smooth, closed, maximally complex submanifold of A. We find a subdomain E of ℂn, depending only on Ω and A, and a complex variety W⊂E such that bW=M in E. Moreover, a generalization to analytic sets of depth at least 4 is given.
Giuseppe Della Sala, Alberto Saracco
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Global Conformal Invariants of Submanifolds [PDF]
Annales de l'Institut Fourier, 2018 The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous example of a global conformal invariant is the Willmore energy of a surface.
Andrea Mondino, Huy The Nguyen
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Some aspects of the global geometry of entire space-like submanifolds [PDF]
Results in Mathematics, 2001 We prove some Bernstein theorems for entire space-like submanifolds in pseudo-Euclidean spaces and, as a corollary, we obtain a new proof of the Calabi-Pogorelov theorem on global solutions of Monge-Ampere equations.
Jürgen Jost, Yuanlong Xin
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Submanifold of a Globally Para framed Metric Manifold [PDF]
Journal of the Tensor Society, 2007 In this paper we have defined various kinds of Hx −connexions and stated and proved many theorems related to them. Some useful results have been derived in the form of corollaries. We have also generalized Gauss Characteristic and Mainardi-Codazzi equations and obtained the equations in the hypersurface therein.
S B Pandey, Savita Patni
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Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds
Hacettepe Journal of Mathematics and Statistics, 2021 We introduce the notion of conformal-twisted product submanifolds of the form $_fM^{T}\times_{b}M^{\theta}$ and $_fM^{\theta}\times_{b}M^{T}$, where $M^T$ is a holomorphic submanifold and $M^\theta$ is a proper slant submanifold of $M$ in a globally conformal Kaehler manifold and $f$ and $b$ are conformal factor and twisting function, respectively. We
Sibel Gerdan Aydın, Hakan Mete Taştan
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Global persistence of Lyapunov-subcenter-manifolds as spectral\n submanifolds under dissipative perturbations [PDF]
SIAM Journal on Applied Dynamical Systems, 2018 For a nondegenerate analytic system with a conserved quantity, a classic result by Lyapunov guarantees the existence of an analytic manifold of periodic orbits tangent to any two-dimensional, elliptic eigenspace of a fixed point satisfying nonresonance conditions.
Rafael de la Llave, Florian Kogelbauer
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Global pinching theorems for minimal submanifolds in spheres [PDF]
Colloquium Mathematicum, 2003 The author proves some rigidity theorems. The framework is a compact submanifold with parallel mean curvature vector embedded in the unit sphere. Sobolev inequalities of P. Li are used as a tool to get estimates for the norms of certain tensors related to the second fundamental form of the compact submanifold conditions for the latter to be a minimal ...
Cai Kai-ren
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Characterizing W 2,p Submanifolds by p -Integrability of Global Curvatures [PDF]
Geometric and Functional Analysis, 2013 We give sufficient and necessary geometric conditions, guaranteeing that an immersed compact closed manifold $ ^m\subset \R^n$ of class $C^1$ and of arbitrary dimension and codimension (or, more generally, an Ahlfors-regular compact set $ $ satisfying a mild general condition relating the size of holes in $ $ to the flatness of $ $ measured in ...
Sławomir Kolasiński +2 more
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