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Special non-Kähler metrics on Endo-Pajitnov manifolds

Cristian Ciulică, Alexandra Otiman, Miron Stanciu

Abstract

We investigate the metric and cohomological properties of higher dimensional analogues of Inoue surfaces, that were introduced by Endo and Pajitnov. We provide a solvmanifold structure and show that in the diagonalizable case, they are formal and have invariant de Rham cohomology. Moreover, we obtain an arithmetic and cohomological characterization of pluriclosed and astheno-Kähler metrics and show they give new examples in all complex dimensions.

Special non-Kähler metrics on Endo-Pajitnov manifolds

Abstract

We investigate the metric and cohomological properties of higher dimensional analogues of Inoue surfaces, that were introduced by Endo and Pajitnov. We provide a solvmanifold structure and show that in the diagonalizable case, they are formal and have invariant de Rham cohomology. Moreover, we obtain an arithmetic and cohomological characterization of pluriclosed and astheno-Kähler metrics and show they give new examples in all complex dimensions.
Paper Structure (5 sections, 12 theorems, 59 equations)

This paper contains 5 sections, 12 theorems, 59 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The solvmanifold structure
  4. de Rham cohomology of $T_M$
  5. Non-Kähler metrics on $T_M$

Key Result

theorem Theorem 3.1

$T_M$ has a natural solvmanifold structure. Specifically, $T_M \simeq { \raisebox{-0.5\faktor@zaehlerhoehe}{${\Gamma}$} \mkern-4mu\diagdown\mkern-5mu \raisebox{0.5\faktor@nennerhoehe}{${G}$} }$, where $G$ is a solvable Lie group of dimension $2n + 2$, $\Gamma \le G$ is a discrete subgroup where $\Delta = \log R^T$ is an upper-triangular matrix and $\Delta_{jj} = \log \beta_j$.

Theorems & Definitions (28)

  • definition Definition 2.1
  • remark Remark 2.1
  • remark Remark 2.2
  • theorem Theorem 3.1
  • proof
  • remark Remark 3.3
  • proposition Proposition 4.1
  • definition Definition 4.2
  • remark Remark 4.4
  • theorem Theorem 4.2
  • ...and 18 more