On the rescaled Riemannian metric of Cheeger Gromoll type on the cotangent bundle

Let $(M,g)$ be an n-dimensional Riemannian manifold and $T^{*}M$ be its cotangent bundle equipped with a Riemannian metric of Cheeger Gromoll type which rescale the horizontal part by a nonzero differentiable function. The main purpose of the present paper is to discuss curvature properties of $T^{*}M$ and construct almost paracomplex Norden structures on $T^{*}M$. We investigate conditions for these structures to be para-K\"ahler (paraholomorphic) and quasi-K\"ahler. Also, some properties of almost paracomplex Norden structures in context of almost product Riemannian manifolds are presented

Paraholomorphic B-manifold and its properties

AbstractThis paper is concerned with problem of the geometry of B-manifolds. We give some properties of Riemannian curvature tensors of paraholomorphic B-manifolds. Finally, we consider some examples of paraholomorphic B-manifolds

Interactions, Strings and Isotopies in Higher Order Anisotropic Superspaces

The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogeneity. The approach proceeds by developing the concept of higher order anisotropic (super)space which unifies the logical and manthematical aspects of modern Kaluza--Klein theories and generalized Lagrange and Finsler geometry and leads to modeling of physical processes on higher order fiber (super)bundles provided with nonlinear and distinguished connections and metric structures. This book can be also considered as a pedagogical survey on the mentioned subjects.Comment: 450 pages, Late