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A survey on submanifolds of nearly Kähler spaces

Mateo Anarella

Abstract

In this survey, we give an introduction to nearly Kähler geometry, and list some results on submanifolds of these spaces. This survey tries by no means to be complete.

A survey on submanifolds of nearly Kähler spaces

Abstract

In this survey, we give an introduction to nearly Kähler geometry, and list some results on submanifolds of these spaces. This survey tries by no means to be complete.
Paper Structure (11 sections, 6 theorems, 7 equations)

This paper contains 11 sections, 6 theorems, 7 equations.

Table of Contents

  1. Introduction
  2. Nearly Kähler manifolds and splitting theorems
  3. Submanifold theory
  4. Submanifolds in the literature
  5. In six dimensional nearly Kähler manifolds
  6. In the nearly Kähler S6
  7. In the nearly Kähler S3xS3
  8. In the nearly Kähler CP3
  9. In the nearly Kähler F(C3)
  10. In pseudo-nearly Kähler manifolds
  11. Personal comments

Key Result

Proposition 1

Two-dimensional and four-dimensional nearly Kähler manifolds are Kähler.

Theorems & Definitions (18)

  • Definition 2.1
  • Proposition 1
  • Proposition 2: Gray '76 gray1, see also nagyfirst
  • Theorem 2.2: Gray '76 gray1
  • Theorem 2.3: Nagy '02 nagyfirst
  • Theorem 2.4: Nagy '02 nagy
  • Theorem 2.5: Butruille '05 butruille
  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • ...and 8 more