From generalized Kaehler to generalized Sasakian structures

TL;DR

This paper introduces and explains various generalized geometric structures on the tangent plus cotangent bundle, including some new properties, serving as an accessible overview for researchers in differential geometry.

Contribution

It provides the first comprehensive introduction to generalized complex, Kaehler, contact, and Sasakian structures, including novel properties within this framework.

Findings

Some properties of generalized structures are newly identified.

The paper offers foundational definitions and characteristic features.

It serves as an expository resource for further research.

Abstract

This is an expository paper, which provides a first introduction to geometric structures on $TM\oplus T^*M$. The paper contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal, almost) contact and generalized Sasakian structures. A few of these properties are new.