# Spherical Submanifolds of a Euclidean Space

## Related Articles

- SUBMANIFOLDS WITH POINTWISE 1-TYPE GAUSS MAP. Kim, Young Ho // Bulletin of the Transilvania University of Brasov, Series III: M;2008, Vol. 1 Issue 50, p201
We introduce the background of the notion of pointwise 1-type Gauss map defined on the submanifolds of a Euclidean space or a pseudo-Euclidean space and the recent results related to it.

- F-Willmore submanifold in space forms. Liu, Jin; Jian, Huaiyu // Frontiers of Mathematics in China;Oct2011, Vol. 6 Issue 5, p871
We introduce an F-Willmore functional of submanifold in space forms, which generalizes the well-known Willmore functional. Its critical point is called the F-Willmore submanifold, for which the variational equation and Simons' type integral inequality are obtained.

- Compact Submanifolds in a Euclidean Space. Deshmukh, Sharief // Open Mathematics Journal;2010, Vol. 3, p1
In this paper we use bounds on the Ricci curvature of an n-dimensional compact submanifold M of the Euclidean space Rn+p to obtain a characterization of a sphere (cf. Theorem 1). Also we obtain a lower bound on the integral of the square of the length of mean curvature vector field H of this...

- Path integration over the n-dimensional Euclidean group. Böhm, M.; Junker, G. // Journal of Mathematical Physics;Jun89, Vol. 30 Issue 6, p1195
The path integral for the n-dimensional free particle is considered. According to the underlying symmetry, the short time propagator is expanded in zonal spherical functions of the Euclidean group G=T n [larger_closed_square] SO(n) with respect to the subgroup H=SO(n). The group theoretical...

- TRANSLATION SURFACES OF WEINGARTEN TYPE IN 3-SPACE. Dillen, Franki; Goemans, Wendy; Van de Woestyne, Ignace // Bulletin of the Transilvania University of Brasov, Series III: M;2008, Vol. 1 Issue 50, p109
In this paper, we derive a classification of translation surfaces in the 3-dimensional Euclidean and Minkowski space, satisfying the Weingarten condition. Even though the family of translation surfaces is one of the simplest to consider, obtaining this classification is far from trivial and...

- Some Identities for Elements of a Symmetric Matrix. Ilyushechkin, N. // Journal of Mathematical Sciences;Sep2005, Vol. 129 Issue 4, p3994
Let Sym (n) be the space of n-dimensional real symmetric matrices and let X ? Sym (n). The matrices E, X, X2,... , Xn - 1 may be considered as vectors of the Euclidean space of dimension n2. Denote by V(E, X,... , Xn - 1) the volume of the parallelepiped spanned by these vectors. It is proved...

- Affine Subspaces of the Lie Algebra se(1,1). Barrett, Dennis I.; Biggs, Rory; Remsing, Claudiu C. // European Journal of Pure & Applied Mathematics;2014, Vol. 7 Issue 2, p140
We classify the full-rank affine subspaces (resp. parametrized affine subspaces) of the semi- Euclidean Lie algebra se(1, 1). The equivalence relations under consideration are motivated by the study of invariant control affine systems. Exhaustive lists of equivalence representatives are...

- Nondegenerate superintegrable systems in n-dimensional Euclidean spaces. Kalnins, E. G.; Kress, J. M.; Miller, W.; Pogosyan, G. S. // Physics of Atomic Nuclei;Mar2007, Vol. 70 Issue 3, p545
We analyze the concept of a nondegenerate superintegrable system in n-dimensional Euclidean space. Attached to this idea is the notion that every such system affords a separation of variables in one of the various types of generic elliptical coordinates that are possible in complex Euclidean...

- Collective Dynamics of Swarms with a New Attraction/Repulsion Function. Hong Shi; Guangming Xie // Mathematical Problems in Engineering;2011, Vol. 2011, Special section p1
We specify an "individual-based" continuous-time model for swarm aggregation in n-dimensional Euclidean space. We show that the swarm is completely stable, and the center of the swarm is stationary. Numerical simulations indicate that the individuals will form a stable and cohesive swarm, and...