Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces real forms of complex algebras, are well-studied in the context symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely, introduce concept pseudo-involution, an automorphism which is only required act involutively on stable Cartan subalgebra, pseudo-fixed-point natural substitute fo...

Using techniques of supersymmetric gauge theories, we present the Ricci-flat metrics on non-compact Kähler manifolds whose conical singularity is repaired by the Hermitian symmetric space. These manifolds can be identified as the complex line bundles over the Hermitian symmetric spaces. Each of the metrics contains a resolution parameter which controls the size of these base manifolds, and the ...

In multidimensional gravity with an arbitrary number of internal Ricci-flat factor spaces, interacting with electric and magnetic p -branes, spherically symmetric configurations are considered. It is shown that all single-brane black hole solutions are stable under spherically symmetric perturbations, whereas similar solutions possessing naked singularities turn out to be catastrophically unsta...

Multidimensional model describing the " cosmological " and/ or spherically symmetric configuration with (n + 1) Einstein spaces in the theory with several scalar fields and forms is considered. When electromagnetic composite p-brane ansatz is adopted, n " internal " spaces are Ricci-flat, one space M 0 has a non-zero curvature, and all p-branes do not " live " in M 0 , a class of exact solution...

We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riema...

Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc-Deslauriers schemes and B-spline schemes. Using a generating function approach, we derive expressions for the symbols of the symmetric m-ary pseudo-spline subdivision schemes. We show that their masks have positive Fourier transform, makin...