Generalized Hsiung–Minkowski formulae on manifolds with density

On some generalized recurrent manifolds

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...

Density estimation on manifolds with boundary

Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation literature is that methods have not been developed for manifolds with boundary, except in simple cases of linear manifolds where the location of the boundary is a...

Generalized Cells in Generalized Manifolds

Multiphase Averaging for Generalized Flows on Manifolds

We present a new proof of a strengthened version of D.V. Anosov's multiphase averaging theorem, originally stated for systems of ODEs with slow variables evolving in R and fast variables evolving on a smooth immersed manifold. Our result allows the fast variables to belong to an arbitrary smooth compact Riemannian manifold, and the vector eld to have only Sobolev regularity. This is accomplishe...

Action of Generalized Lie Groups on Manifolds

In this paper by definition of generalized action of generalized Lie groups (top spaces) on a manifold, the concept of stabilizer of the top spaces is introduced. We show that the stabilizer is a top space, moreover we find the tangent space of a stabilizer. By using of the quotient spaces, the dimension of some top spaces are fined.