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Periodica Mathematica Hungarica, 2000
A diffeomorphism \(\delta:M\to M\) of a boundaryless \(k\)-dimensional submanifold \(M\) of a Euclidean space \(\mathbb{R}^n\) is called by the authors diametrical with respect to the center \(p\) if \(x\), \(p\) and \(\delta(x)\) \((x\in M)\) are distinct collinear points and \(T_x M=T_{\delta(x)} M\).
Craveiro de Carvalho, F. J. +1 more
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A diffeomorphism \(\delta:M\to M\) of a boundaryless \(k\)-dimensional submanifold \(M\) of a Euclidean space \(\mathbb{R}^n\) is called by the authors diametrical with respect to the center \(p\) if \(x\), \(p\) and \(\delta(x)\) \((x\in M)\) are distinct collinear points and \(T_x M=T_{\delta(x)} M\).
Craveiro de Carvalho, F. J. +1 more
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Journal of Geometric Analysis, 2011
From the author's abstract: We propose an answer to a question raised by F. Burstall: Is there any interesting theory of isothermic submanifolds of \(\mathbb{R}^n\) of dimension greater than two? We call an \(n\)-immersion \(f(x)\) in \(\mathbb{R}^m\) isothermic\(_k\) if the normal bundle of \(f\) is flat and \(x\) is a line of curvature coordinate ...
Donaldson, Neil, Terng, Chuu-Lian
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From the author's abstract: We propose an answer to a question raised by F. Burstall: Is there any interesting theory of isothermic submanifolds of \(\mathbb{R}^n\) of dimension greater than two? We call an \(n\)-immersion \(f(x)\) in \(\mathbb{R}^m\) isothermic\(_k\) if the normal bundle of \(f\) is flat and \(x\) is a line of curvature coordinate ...
Donaldson, Neil, Terng, Chuu-Lian
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Journal of Geometry, 1993
Generalized Chen submanifolds or \(k\)-th Chen submanifolds are defined. The authors give a characterization of those submanifolds in terms of an operator of J. Simons. They relate these submanifolds to submanifolds of finite type introduced by B. Y. Chen and prove that: Let \(M\) be a compact submanifold in \(E^ m\) with parallel second fundamental ...
Li, Shi-Jie, Houh, Chorng-Shi
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Generalized Chen submanifolds or \(k\)-th Chen submanifolds are defined. The authors give a characterization of those submanifolds in terms of an operator of J. Simons. They relate these submanifolds to submanifolds of finite type introduced by B. Y. Chen and prove that: Let \(M\) be a compact submanifold in \(E^ m\) with parallel second fundamental ...
Li, Shi-Jie, Houh, Chorng-Shi
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2004
Abstract The prototypical submanifold is a surface in ordinary space. There are various ways of describing surfaces in ordinary space.
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Abstract The prototypical submanifold is a surface in ordinary space. There are various ways of describing surfaces in ordinary space.
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SUT Journal of Mathematics, 2001
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Geometriae Dedicata, 1986
The author generalizes the definition of isoparametric submanifolds to higher codimensions as follows: a submanifold is isoparametric if the eigenvalues of the shape operator are constant along all parallel curves of normal vectors. Other definitions have been given by \textit{J. Eells} [On equivariant harmonic maps, Proc. Conf. Differ. Geom.
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The author generalizes the definition of isoparametric submanifolds to higher codimensions as follows: a submanifold is isoparametric if the eigenvalues of the shape operator are constant along all parallel curves of normal vectors. Other definitions have been given by \textit{J. Eells} [On equivariant harmonic maps, Proc. Conf. Differ. Geom.
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Journal of Geometric Analysis, 1994
Let \(M\) be a manifold endowed with a symmetric tensor field \(g\) of type \((0,2)\). Denote by \(S\) the set of points of degeneracy for \(g\). The author obtains an existence and uniqueness theorem for geodesics through \(S\) and existence and uniqueness theorems for parallel and Jacobi fields along these geodesics.
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Let \(M\) be a manifold endowed with a symmetric tensor field \(g\) of type \((0,2)\). Denote by \(S\) the set of points of degeneracy for \(g\). The author obtains an existence and uniqueness theorem for geodesics through \(S\) and existence and uniqueness theorems for parallel and Jacobi fields along these geodesics.
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Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms
Mathematics, 2023Yanlin Li +2 more
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