Structures Which are Harmonic with Respect to Walker Metrics

Let ( W , q , D ) be a Walker manifold. We find all Walker metrics which are harmonic [in the sense of Chen and Nagano in (J Math Soc Jpn 36:295–313, 1984 )] w.r.t. q . On the total space of the tangent bundle of W , we obtain necessary and sufficient conditions concerning the harmonicity of certain...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 12; no. 2; pp. 481 - 496
Main Authors Bejan, Cornelia-Livia, Druţă-Romaniuc, Simona-Luiza
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.05.2015
Subjects
Mathematics
Mathematics and Statistics
Primary 53C43
harmonic maps
mixed 3-structures
58E20
53C55
53C05
53C15
Walker manifold
Harmonic function
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Summary:Let ( W , q , D ) be a Walker manifold. We find all Walker metrics which are harmonic [in the sense of Chen and Nagano in (J Math Soc Jpn 36:295–313, 1984 )] w.r.t. q . On the total space of the tangent bundle of W , we obtain necessary and sufficient conditions concerning the harmonicity of certain metrics w.r.t. the Sasaki (resp. horizontal, vertical) lift of q . The harmonicity in the sense of García-Río et al. in (Ill J Math 41(1):23–30, 1997 ) of the three endomorphism fields of an almost hyper-para-Hermitian structure is characterized. As an application, we deal with mixed 3-structures, a notion for which we quote Ianuş in (Mediterr J Math 3(3–4):581–592, 2006 ).
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-014-0409-y