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Invariance Principle for Lifts of Geodesic Random Walks. [PDF]
J Theor ProbabJunné J, Redig F, Versendaal R.
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Riemannian Newton Methods for Energy Minimization Problems of Kohn-Sham Type. [PDF]
J Sci ComputAltmann R, Peterseim D, Stykel T.
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Data-driven modeling of subharmonic forced response due to nonlinear resonance. [PDF]
Sci RepAxås J +3 more
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Submanifold-Preserving Discriminant Analysis With an Auto-Optimized Graph
IEEE Transactions on Cybernetics, 2020Due to the multimodality of non-Gaussian data, traditional globality-preserved dimensionality reduction (DR) methods, such as linear discriminant analysis (LDA) and principal component analysis (PCA) are difficult to deal with.
F. Nie, Z. Wang, Rong Wang, Xuelong Li
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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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A bound on the dimension of a totally geodesic submanifold in the Prym locus
, 2017We give an upper bound for the dimension of a germ of a totally geodesic submanifold, and hence of a Shimura variety of $${{\mathcal {A}}}_{g-1}$$Ag-1, contained in the Prym locus. First we give such a bound for a germ passing through a Prym variety of a
E. Colombo, P. Frediani
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Volume Growth, Number of Ends, and the Topology of a Complete Submanifold
, 2011Given a complete isometric immersion φ:Pm⟶Nn in an ambient Riemannian manifold Nn with a pole and with radial sectional curvatures bounded from above by the corresponding radial sectional curvatures of a radially symmetric space $M^{n}_{w}$, we determine
V. Gimeno, V. Palmer
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