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The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces
Fischer decomposition Clifford analysis Hodge-de Rham equation spherical monogenics
2011/2/25
The classical Fischer decomposition of spinor-valued polynomials is a key result on solutions of the Dirac equation in the Euclidean space Rm.As is well-known, it can be understood as an irreducible d...
Hypersurfaces with small extrinsic radius or large $\lambda_1$ in Euclidean spaces
Mean curvature Reilly inequality Laplacian Spectrum pinching results
2010/12/3
We prove that hypersurfaces of Rn+1 which are almost extremal for the
Reilly inequality on 1 and have Lp-bounded mean curvature (p > n) are Hausdorff close to a sphere, have almost constant mean cur...
Our main result states that every fixed-point free continuous self-map of ${\mathbb R}^{n}$ is colorable. This result can be re-formulated as follows: A continuous map $f: {\mathbb R}^{n}\to {\mathbb...
Realization of Frobenius manifolds as submanifolds in pseudo-Euclidean spaces
k-potential submanifolds partial differential equations pseudo-Euclidean spaces
2010/4/8
We introduce a class of k-potential submanifolds in pseudo-Euclidean spaces and prove that for an arbitrary positive integer k and an arbitrary nonnegative integer p, each N-dimensional Frobenius mani...
Lightlike Hypersurfaces of Semi-Euclidean Spaces Satisfying Curvature Conditions of Semisymmetry Type
Degenerate metric Screen conformal lightlike hypersurface Parallel lightlike hypersurface Semi-symmetric lightlike hypersurface
2010/2/26
In this paper, we investigate lightlike hypersurfaces which are semi-symmetric, Ricci semi-symmetric, parallel or semi-parallel in a semi-Euclidean space. We obtain that every screen conformal lightli...