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On isometric immersions of sub-Riemannian manifolds

Vladimir Rovenski
Dec 2022
摘要
We study curvature invariants of a sub-Riemannian manifold (i.e., a manifoldwith a Riemannian metric on a non-holonomic distribution) related to mutualcurvature of several pairwise orthogonal subspaces of the distribution, andprove geometrical inequalities for a sub-Riemannian submanifold. Asapplications, inequalities are proved for submanifolds with mutually orthogonaldistributions that include scalar and mutual curvature. For compactsubmanifolds, inequalities are obtained that are supported by known integralformulas for almost-product manifolds.
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