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Norden Golden Manifolds with Constant Sectional Curvature and Their Submanifolds

Author

Listed:
  • 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)

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.

Suggested Citation

  • Fulya Şahin & Bayram Şahin & Feyza Esra Erdoğan, 2023. "Norden Golden Manifolds with Constant Sectional Curvature and Their Submanifolds," Mathematics, MDPI, vol. 11(15), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3301-:d:1203783
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