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math.DG2021
Homology vanishing theorems for pinched submanifolds
Christos-Raent Onti, Theodoros Vlachos
We investigate the geometry and topology of submanifolds under a sharp pinching condition involving extrinsic invariants like the mean curvature and the length of the second fundam…
math.DG2021
A class of Einstein submanifolds of Euclidean space
M. Dajczer, C. -R. Onti, Th. Vlachos
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…
math.DG2021
On constant curvature submanifolds of space forms
M. Dajczer, C. -R. Onti, Th. Vlachos
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 s…