Some Para-Hermitian Related Complex Structures and Non-existence of Semi-Riemannian Metric on Some Spheres

Erdem, Sadettin

Serdica Mathematical Journal (1999)

  • Volume: 25, Issue: 1, page 83-90
  • ISSN: 1310-6600

Abstract

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It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4) can be given neither an indefinite metric of any signature (resp: of signature (r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further for every given Riemannian metric on an almost para-Hermitian manifold with the associated 2-form φ one can construct an almost Hermitian structure (under certain conditions, two different almost Hermitian structures) whose associated 2-form(s) is φ.

How to cite

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Erdem, Sadettin. "Some Para-Hermitian Related Complex Structures and Non-existence of Semi-Riemannian Metric on Some Spheres." Serdica Mathematical Journal 25.1 (1999): 83-90. <http://eudml.org/doc/11506>.

@article{Erdem1999,
abstract = {It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4) can be given neither an indefinite metric of any signature (resp: of signature (r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further for every given Riemannian metric on an almost para-Hermitian manifold with the associated 2-form φ one can construct an almost Hermitian structure (under certain conditions, two different almost Hermitian structures) whose associated 2-form(s) is φ.},
author = {Erdem, Sadettin},
journal = {Serdica Mathematical Journal},
keywords = {Hermitian; Para-Hermitian and Indefinite Metric; indefinite metric; para-Hermitian manifold; almost paracomplex structure},
language = {eng},
number = {1},
pages = {83-90},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Some Para-Hermitian Related Complex Structures and Non-existence of Semi-Riemannian Metric on Some Spheres},
url = {http://eudml.org/doc/11506},
volume = {25},
year = {1999},
}

TY - JOUR
AU - Erdem, Sadettin
TI - Some Para-Hermitian Related Complex Structures and Non-existence of Semi-Riemannian Metric on Some Spheres
JO - Serdica Mathematical Journal
PY - 1999
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 25
IS - 1
SP - 83
EP - 90
AB - It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4) can be given neither an indefinite metric of any signature (resp: of signature (r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further for every given Riemannian metric on an almost para-Hermitian manifold with the associated 2-form φ one can construct an almost Hermitian structure (under certain conditions, two different almost Hermitian structures) whose associated 2-form(s) is φ.
LA - eng
KW - Hermitian; Para-Hermitian and Indefinite Metric; indefinite metric; para-Hermitian manifold; almost paracomplex structure
UR - http://eudml.org/doc/11506
ER -

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