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math.DG2017
Einstein submanifolds with flat normal bundle in space forms are holonomic
M. Dajczer, C. -R. Onti, Th. Vlachos
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)…
math.DG2017
Einstein submanifolds with parallel mean curvature
Christos-Raent Onti
We provide a classification of Einstein submanifolds in space forms with flat normal bundle and parallel mean curvature. This extends a previous result due to Dajczer and Tojeiro f…
math.DG2017
Topological obstructions for submanifolds in low codimension
Christos-Raent Onti, Theodoros Vlachos
We prove integral curvature bounds in terms of the Betti numbers for compact submanifolds of the Euclidean space with low codimension. As an application, we obtain topological obst…