Geodesic
A study concerning Berger type deformed Sasaki metric on the tangent bundle
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019), pp. 435-447

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Let $TM$ be the tangent bundle over an almost anti-paraHermitian manifold endowed with Berger type deformed Sasaki metric $g_{BS}$. In this paper, first, we obtain the Levi-Civita connection of this metric and study geodesics on $TM$. Secondly, we construct some almost anti-paraHermitian structures on $TM$ and search conditions for these structures to be anti-paraKähler and quasi-anti-paraKähler. Finally, we present certain Riemannian curvature properties of $(TM,g_{BS})$. 
@article{JMAG_2019_15_a0,
     author = {Murat Altunbas and Ramazan Simsek and Ayd{\i}n Gezer},
     title = {A study concerning {Berger} type deformed {Sasaki} metric on the tangent bundle},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {435--447},
     publisher = {mathdoc},
     volume = {15},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2019_15_a0/}
}
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Murat Altunbas; Ramazan Simsek; Aydın Gezer. A study concerning Berger type deformed Sasaki metric on the tangent bundle. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019), pp. 435-447. http://geodesic.mathdoc.fr/item/JMAG_2019_15_a0/