41 research outputs found
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