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A Boothby-Wang construction in generalized contact geometry

Debjit Pal

Abstract

We establish a generalized analogue of the Boothby-Wang theorem in generalized contact geometry, along with related results. We present a general method for constructing examples of generalized contact structures that are not of Poon-Wade type, and even examples that fail to be generalized contact structures. Using Courant reduction methods, we construct a generalized complex structure on a smooth leaf space and equip the generalized contact manifold with a principal bundle structure whose connection is defined by the generalized contact data. Under mild assumptions, we show that the curvature induces a symplectic foliation on the leaf space. Several examples are provided.

A Boothby-Wang construction in generalized contact geometry

Abstract

We establish a generalized analogue of the Boothby-Wang theorem in generalized contact geometry, along with related results. We present a general method for constructing examples of generalized contact structures that are not of Poon-Wade type, and even examples that fail to be generalized contact structures. Using Courant reduction methods, we construct a generalized complex structure on a smooth leaf space and equip the generalized contact manifold with a principal bundle structure whose connection is defined by the generalized contact data. Under mild assumptions, we show that the curvature induces a symplectic foliation on the leaf space. Several examples are provided.
Paper Structure (10 sections, 20 theorems, 149 equations)

This paper contains 10 sections, 20 theorems, 149 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Generalized complex structures
  4. Generalized contact structures
  5. Boothby-Wang construction
  6. Induced Principal bundle structures
  7. Induced generalized complex structures
  8. Observations and examples
  9. Generalized contact manifolds of Poon-Wade type
  10. Construction for new examples of non Poon-Wade types

Key Result

Theorem 1

Theorems & Definitions (70)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Definition 2.1
  • Definition 2.2
  • Example 2.3
  • Example 2.4
  • Definition 2.5
  • Theorem 2.6
  • Definition 2.7
  • ...and 60 more