We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

In this paper an almost paracomplex structures on the coframe bundle with Cheeger- Gromoll metric are defined and later we obtained integrability conditions of these structures. Also proved that para-Norden which exists non-Kahler-Norden.

Recall that mirror symmetry predicts the existence of pairs X, X̌ of Calabi-Yau manifolds whose Hodge diamonds are mirror images of each other, i.e. H(X,ΛTX) ' H(X̌,ΩX̌). In fact, mirror symmetry reflects much more than just the Hodge structures, and we also get an isomorphism between the “Yukawa couplings” on H(X,TX) and H(X̌), which give product structures H(X,TX)⊗H(X,TX)→ H(X,TX) and H(X̌)⊗H(X̌)→ ...

Effective actions are derived for (2,0) and (2,1) superstrings by studying the corresponding sigma-models. The geometry is a generalisation of Kahler geometry involving torsion and the field equations imply that the curvature with torsion is self-dual in four dimensions, or has SU(n, m) holonomy in other dimensions. The Yang-Mills fields are self-dual in four dimensions and satisfy a form of th...

This paper details the techniques and algorithms implemented in Kahler, a Python library that implements discrete exterior calculus on arbitrary Hermitian manifolds. Borrowing techniques and ideas first implemented in PyDEC, Kahler provides a uniquely general framework for computation using discrete exterior calculus. Manifolds can have arbitrary dimension, topology, bilinear Hermitian metrics,...

We state a general conjecture about the existence of Kahler metrics of constant scalar curvature, and discuss the background to the conjecture 1. The equations In this article we discuss some well-known problems in Kahler geometry. The general theme is to ask whether a complex manifold admits a preferred Kahler metric, distinguished by some natural differential-geometric criterion. A paradigm i...

Gordon and Benson have proved that if a compact nilmanifold admits a Kahler structure then it is a torus [5] more precisely they proved that the condition (iv) fails for any symplectic structure on a non-toral nilmanifold M. This result was independently proved by Hasegawa [12] by showing that (v) fails for M. For a compact solvmanifold M of dimension 4 it is known that M has a Kahler structure...