A characterization of the Riemann extension in terms of harmonicity

Title:

A characterization of the Riemann extension in terms of harmonicity

Creator:

Bejan, Cornelia-Livia and Eken, Şemsi

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a5e89635-9ec1-425a-b3db-cba928d35de8
uuid:a5e89635-9ec1-425a-b3db-cba928d35de8
issn:0011-4642

Subject:

matematika, mathematics, harmonické tenzorové pole, Semi-Riemannian manifold, cotangent bundle, natural Riemann extension, harmonic tensor field, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

If (M,∇) is a manifold with a symmetric linear connection, then T*M can be endowed with the natural Riemann extension g¯ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to g¯g¯ initiated by C. L.Bejan and O.Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure PP on (T*M, g¯) and prove that P is harmonic (in the sense of E.Garciá-Río, L.Vanhecke and M. E.Vázquez-Abal (1997)) if and only if g¯ reduces to the classical Riemann extension introduced by E.M. Patterson and A.G. Walker (1952)., Cornelia-Livia Bejan, Şemsi Eken., and Obsahuje bibliografii

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

197-206

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:1

Harvested from:

CDK

Metadata only:

false