Norden Golden Manifolds with Constant Sectional Curvature and Their Submanifolds

Fulya Şahin, Bayram Şahin () and Feyza Esra Erdoğan
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Fulya Şahin: Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey
Bayram Şahin: Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey
Feyza Esra Erdoğan: Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey

Mathematics, 2023, vol. 11, issue 15, 1-10

Abstract: This paper discusses the Norden golden manifold having a constant sectional curvature. First, it is shown that if a Norden golden manifold has a constant real sectional curvature, the manifold is flat. For this reason, the notions of holomorphic-like sectional curvature and holomorphic-like bisectional curvature on the Norden golden manifold are investigated, but it is seen that these notions do not work on the Norden golden manifold. This shows the need for a new concept of sectional curvature. In this direction, a new notion of sectional curvature (Norden golden sectional curvature) is proposed, an example is given, and if this new sectional curvature is constant, the curvature tensor field of the Norden golden manifold is expressed in terms of the metric tensor field. Since the geometry of the submanifolds of manifolds with constant sectional curvature has nice properties, the last section of this paper examines the semi-invariant submanifolds of the Norden golden space form.

Keywords: semi-Riemannian manifold; sectional curvature; space form; golden manifold; Norden golden manifold; semi-invariant submanifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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