From pseudo-holomorphic functions to the associated real manifold

This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the differential inequalities describing pseudo-holomorphic functions can be used to define a one-real-dimensional manifold (by the vanishing of a function with nonzero gradient), which is here a 1-parameter family of plane curves. On studying the associated envelopes, such a parameter can be eliminated by solving two nonlinear partial differential equations. The classical differential geometry of curves can be therefore exploited to get a novel perspective on the equations describing the global theory of pseudo-holomorphic functions.Comment: 25 page

Select Topics in Quantum Gravity : A Maiden Voyage

We study selected aspects of Theoretical Physics confronting some key issues related to the fundamental interactions along the line of Black Holes (BHs) and Attractors and its thread may be found in the concepts of Supersymmetry, Supergravity and Holography which encompass all of String theory and Quantum gravity. Then we also had an encounter with maximally symmetric spaces in General Relativity such as de Sitter and we did some significant computation in this backdrop which is tempting to pursue keeping in mind the recent observational data in favor of inflationary picture of the Universe