This is a short version of the author’s habilitation thesis. The main results have been published but many details are developed and clarified. As well some new results are included: we additionally discuss here quasi classical limit of ALG(a) quantization, mention some topological properties of the moduli space of Bohr Sommerfeld Lagrangian cycles of fixed volume and investigate some propertie...

In this paper, we examine the proper semi-slant pseudo-Riemannian submersions in para-Kaehler geometry and prove some fundamental results on such submersions. particular obtain curvature relations space forms. Moreover, provide examples of

we obtain the expression of ricci tensor for a $gcr$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $gcr$-lightlike submanifold of anindefinite complex space form. moreover, we have proved that everyproper totally umbilical $gcr$-lightlike submanifold of anindefinite kaehler manifold is a totally geodesic $gcr$-lightlikesubmanifold.