Study extends isometric immersions using submanifolds.
problem General extension problem for isometric immersions.
method Establishing Cartan-Ambrose-Hicks theorems based on submanifolds.
result Geometric constructions of isometric extensions.
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4 results for “Cartan-Ambrose-Hicks”
Extends submanifold theorem to general spaces.
problem Tackles submanifolds in general ambient spaces.
method Uses development of curves in positive codimension and generalizes Cartan-Ambrose-Hicks theorem.
result Provides a geometric construction of isometric immersions.
Using the notion of Levi form of a smooth distribution, we discuss the local and the global problem of existence of one horizontal section of a smooth vector bundle endowed with a horizontal distribution. The analysis will lead to the formulation of a "one-leaf" analogue of the classical Frobenius integrability theorem…
We show that for an arbitrarily given closed Riemannian manifold admitting a point with a single cut point, every closed Riemannian manifold admitting a point with a single cut point is diffeomorphic to if the radial curvatures of at are sufficiently close in the sense of -n…