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Keywords:
reflections; isometric flows; transversally symmetric immersions; locally transversally symmetric submanifolds; (locally) symmetric and transversally symmetric immersions and submanifolds; Killing-transversally symmetric spaces; normal flow space forms
reflections; isometric flows; transversally symmetric immersions; locally transversally symmetric submanifolds; (locally) symmetric and transversally symmetric immersions and submanifolds; Killing-transversally symmetric spaces; normal flow space forms
Summary:
We introduce the notions of (extrinsic) locally transversally symmetric immersions and submanifolds in a Riemannian manifold equipped with a unit Killing vector field as analogues of those of (extrinsic) locally symmetric immersions and submanifolds. We treat their geometric properties, derive several characterizations and give a list of examples.
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