… This paper considers two intertwined submanifolds within the same high-dimensional
space. Assume that a dataset X ⊂ RD is embedded in two submanifolds: 1) ϒ and 2) …

… submanifolds of space forms, the relative nullity distribution, principal normal vector fields and
submanifolds … and the Fundamental theorem of submanifolds, namely, the Burstin– Mayer–…

… However, the theory of submanifolds given in this book is relatively new in … The normal
connection of submanifolds play an important role in this chapter. … We may then decompose Vx; as …

This paper investigates decompositions of boundaryless manifolds into closed, connected,
codimension one submanifolds. It was inspired by recent work of VT Liem [22], with a related …

… immersion X (or the submanifold M) is said to be of k-type and the decomposition (1.1) is
called … Let X : M -+ Em be a k-type immersion with its spectral decomposition given by (1.1). We …

… , then these foliations are parallel and de Rham's decomposition theorem ([9]) asserts that …
orthogonal foliations whose leaves are totally umbilic submanifolds. In this case the manifold …

We remark that if X’and Y" are respectively the (1,) and (o, 1) components of X and Y with
respect to the decomposition (1), we have so that (1, 1)-geodesic maps are also characterized …

… novel submanifold decomposition (SMD) algorithm, which simultaneously considers multiple
submanifolds … We investigate the sub-manifold decomposition problem which has not been …

… conditions about decompositions into submanifolds under which the decomposition map
is … Sections 3 and 5 present the main results, the former about decompositions of 4-manifolds …

… A Riemannian submanifold M is a totally geodesic submanifold of M if and only if every
geodesic of M is a geodesic of M Let M be a submanifold of M and let e 1 ,…, e n be an …