Zobrazeno 1 - 10
of 65
pro vyhledávání: '"Vlachos, Th."'
We investigate specific intrinsic curvatures $\rho_k$ (where $1\leq k\leq n$) that interpolate between the minimum Ricci curvature $\rho_1$ and the normalized scalar curvature $\rho_n=\rho$ of $n$-dimensional Riemannian manifolds. For $n$-dimensional
Externí odkaz:
http://arxiv.org/abs/2406.11692
Autor:
Dajczer, M., Vlachos, Th.
We identify as topological spheres those complete submanifolds lying with any codimension in hyperbolic space whose Ricci curvature satisfies a lower bound contingent solely upon the length of the mean curvature vector of the immersion.
Externí odkaz:
http://arxiv.org/abs/2404.14023
Let the warped product $M^n=L^m\times_\varphi F^{n-m}$, $n\geq m+3\geq 8$, of Riemannian manifolds be an Einstein manifold with Ricci curvature $\rho$ that admits an isometric immersion into Euclidean space with codimension two. Under the assumption
Externí odkaz:
http://arxiv.org/abs/2210.09568
In this paper we give local and global parametric classifications of a class of Einstein submanifolds of Euclidean space. The highlight is for submanifolds of codimension two since in this case our assumptions are only of intrinsic nature.
Externí odkaz:
http://arxiv.org/abs/2103.00224
We prove a converse to well-known results by E. Cartan and J. D. Moore. Let $f\colon M^n_c\to\Q^{n+p}_{\tilde c}$ be an isometric immersion of a Riemannian manifold with constant sectional curvature $c$ into a space form of curvature $\tilde c$, and
Externí odkaz:
http://arxiv.org/abs/2101.03586
We investigate the behavior of the second fundamental form of an isometric immersion of a space form with negative curvature into a space form so that the extrinsic curvature is negative. If the immersion has flat normal bundle, we prove that its sec
Externí odkaz:
http://arxiv.org/abs/2008.03929
In the realm of conformal geometry, we give a classification of the Euclidean hypersurfaces that admit a non-trivial conformal infinitesimal variation. In the restricted case of conformal variations, such a classification was obtained by E. Cartan in
Externí odkaz:
http://arxiv.org/abs/2005.05016
Autor:
Kanellopoulou, A. E., Vlachos, Th.
In this paper, we investigate geometric conditions for isometric immersions with positive index of relative nullity to be cylinders. There is an abundance of noncylindrical $n$-dimensional minimal submanifolds with index of relative nullity $n-2$, fu
Externí odkaz:
http://arxiv.org/abs/2001.11417
Autor:
Dajczer, M., Vlachos, Th.
Austere submanifolds of Euclidean space were introduced in 1982 by Harvey and Lawson in their foundational work on calibrated geometries. In general, the austerity condition is much stronger than minimality since it express that the nonzero eigenvalu
Externí odkaz:
http://arxiv.org/abs/1902.06058
A well-known result asserts that any isometric immersion with flat normal bundle of a Riemannian manifold with constant sectional curvature into a space form is (at least locally) holonomic. In this note, we show that this conclusion remains valid fo
Externí odkaz:
http://arxiv.org/abs/1712.05462