Geodesic
Some notes on metallic Kähler manifolds
Filomat, Tome 35 (2021) no. 6, p. 1963

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DOI

The present paper deals with metallic Kähler manifolds. Firstly, we define a tensor H which can be written in terms of the (0, 4)−Riemannian curvature tensor and the fundamental 2−form of a metallic Kähler manifold and study its properties and some hybrid tensors. Secondly, we obtain the conditions under which a metallic Hermitian manifold is conformal to a metallic Kähler manifold. Thirdly, we prove that the conformal recurrency of a metallic Kähler manifold implies its recurrency and also obtain the Riemannian curvature tensor form of a conformally recurrent metallic Kähler manifold with non-zero scalar curvature. Finally, we present a result related to the notion of Z recurrent form on a metallic Kähler manifold.
DOI : 10.2298/FIL2106963G
Classification : 53C15, 53C55
Keywords: Conformal recurrency, conformal transformation, metallic Kähler manifold, hybrid tensor, Z−form 
Aydin Gezer; Fatih Topcuoglu; Uday C; and De. Some notes on metallic Kähler manifolds. Filomat, Tome 35 (2021) no. 6, p. 1963 . doi: 10.2298/FIL2106963G
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     author = {Aydin Gezer and Fatih Topcuoglu and Uday C and and De},
     title = {Some notes on metallic {K\"ahler} manifolds},
     journal = {Filomat},
     pages = {1963 },
     year = {2021},
     volume = {35},
     number = {6},
     doi = {10.2298/FIL2106963G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2106963G/}
}
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