Ayush Jaiswal

Indian Institute of Science Education and Research, Tirupati · Mathematics

In this article, we will explore the fundamental concepts, including various basic concepts on $d$-complex manifolds, along with several differential operators and examine the relationships between them. A $d$-K\"ahler manifold is a $d$-complex manifold equipped with a metric that satisfies a specific condition. We prove the Hodge decomposition the...

We develop the theory of d-holomorphic connections on d-holomorphic vector bundles over Klein surfaces by constructing the analogous Atiyah exact sequence for d-holomorphic bundles. We also give a criterion for the existence of d-holomorphic connection in d-holomorphic bundle over a Klein surface in the spirit of the Atiyah–Weil criterion for holom...

In this article, we study the gauge theoretic aspects of real and quaternionic parabolic bundles over a real curve $(X, \sigma_X)$, where X is a compact Riemann surface and {\sigma}X is an anti-holomorphic involution. For a fixed real or quaternionic structure on a smooth parabolic bundle, we examine the orbits space of real or quaternionic connect...