Abstract
We consider proper CR‐submanifolds of the six‐dimensional sphere S6. We prove that S6 does not admit compact proper CR‐submanifolds with non‐negative sectional curvature and integrable holomorphic distribution.
Highlights
We prove that S6 does not admit compact proper CR-submanifolds with non-negative sectional curvature and integrable holomorphic distribution
The study of CR-submanifolds of a Kaehler manifold was initiated by Bejancu [1]
CR-submanifolds of S have been studied by several mathematicians
Summary
The study of CR-submanifolds of a Kaehler manifold was initiated by Bejancu [1]. This study generalizes both the complex submanifolds as well as the totally real submanifolds. We consider proper CR-submanifolds of the six-dimensional sphere S6. We prove that S6 does not admit compact proper CR-submanifolds with non-negative sectional curvature and integrable holomorphic distribution. CR-submanifolds, Kaehler manifold, nearly Kaehler manifold, the six-dimensional sphere, almost complex structures. The study of CR-submanifolds of a Kaehler manifold was initiated by Bejancu [1].
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