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On Almost Hyper-Para-Kähler Manifolds
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-03-08
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
In this paper it is shown that a 2n-dimensional almost symplectic manifold (M,ω) can be endowed with an almost paracomplex structure K, K2=IdTM, and an almost complex structure J, J2=-IdTM, satisfying ω(JX,JY)=ω(X,Y)=-ω(KX,KY) for X,Y∈TM, ω(X,JX)>0 for X≠0 and KJ=-JK, if and only if the structure group of TM can be reduced from Sp(2n) (or U(n)) to O(n).
In the symplectic case such a manifold (M,ω,J,K) is called an almost hyper-para-Kähler manifold.
Topological and metric properties of almost hyper-para-Kähler manifolds as well as integrability of (J,K) are discussed.
It is especially shown that the Pontrjagin classes of the eigenbundles P± of K to the eigenvalues ±1 depend only on the symplectic structure and not on the choice of K.
American Psychological Association (APA)
Merker, Jochen. 2012. On Almost Hyper-Para-Kähler Manifolds. ISRN Geometry،Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-479416
Modern Language Association (MLA)
Merker, Jochen. On Almost Hyper-Para-Kähler Manifolds. ISRN Geometry No. 2012 (2012), pp.1-13.
https://search.emarefa.net/detail/BIM-479416
American Medical Association (AMA)
Merker, Jochen. On Almost Hyper-Para-Kähler Manifolds. ISRN Geometry. 2012. Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-479416
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-479416