We describe analytic pencils of conics passing through the origin in C that can be mapped to straight lines locally near the origin by an analytic diffeomorphism. Under a minor non-degeneracy assumption, we prove that in a pencil with this property, almost all conics have 3 points of tangency with the same algebraic curve of class 3 (i. e. a curve projectively dual to a cubic). 2000 Math. Subj....

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

In this paper we study *-Conformal {\eta}-Ricci soliton on Sasakian manifolds. Here, discuss some curvature properties manifold admitting soliton. We obtain significant results in manifolds satisfying R({\xi},X).S = 0, S({\xi},X).R {\overline}P({\xi},X).S where {\overline}P is Pseudo-projective tensor.The conditions for {\Phi}-conharmonically flat and {\Phi}-projectively have been obtained arti...

This article is a survey of recent work [15, 6, 7, 13] developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential geometry: given a smooth manifold M endowed with a flat conformal/projective structure, we establish a canonical isomorphism between the space of symmetric contravar...