Non-existence of CR submanifolds of maximal CR dimension satisfying RA = 0 in non-flat complex space forms
Mirjana Milijevic
TL;DR
This paper extends the non-existence result of real hypersurfaces with zero shape operator to CR submanifolds of maximal CR dimension in non-flat complex space forms, showing such submanifolds do not exist.
Contribution
It proves the non-existence of CR submanifolds of maximal CR dimension satisfying RA=0 in non-flat complex space forms, generalizing previous results for real hypersurfaces.
Findings
No CR submanifolds of maximal CR dimension satisfy RA=0 in non-flat complex space forms.
Extends non-existence results from real hypersurfaces to CR submanifolds.
Supports the understanding of geometric constraints in complex space forms.
Abstract
It has been proved that there are no real hypersurfaces satisfying RA = 0 in non-flat complex space forms. In this paper we prove that the same is true in the case of CR submanifolds of maximal CR dimension, that is there are no CR submanifolds of maximal CR dimension satisfying RA = 0 in non-flat complex space forms.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometric Analysis and Curvature Flows · Geometry and complex manifolds