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Oğuzhan Bahadır

Bio: Oğuzhan Bahadır is an academic researcher from Kahramanmaraş Sütçü İmam University. The author has contributed to research in topics: Metric connection & Statistical manifold. The author has an hindex of 4, co-authored 21 publications receiving 56 citations.

Papers
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Journal ArticleDOI
01 Sep 2019
TL;DR: In this paper, the authors define and study statistical solitons on Ricci-symmetric statistical warped products and establish a relationship between the scalar curvature and the Casorati curvatures in terms of the Laplacian of the warping function for statistical warped product submanifolds.
Abstract: Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products R × f N 2 and N 1 × f R . Second, we study statistical warped products as submanifolds of statistical manifolds. For statistical warped products statistically immersed in a statistical manifold of constant curvature, we prove Chen’s inequality involving scalar curvature, the squared mean curvature, and the Laplacian of warping function (with respect to the Levi–Civita connection). At the end, we establish a relationship between the scalar curvature and the Casorati curvatures in terms of the Laplacian of the warping function for statistical warped product submanifolds in the same ambient space.

21 citations

Journal ArticleDOI
TL;DR: A class of lightlike hypersurfaces is introduced called screen semi-invariant light like hypersurface and radical anti-invARIant lightlike Hypersurface with respect to a quarter-symmetric nonmetric connection which is determined by the product structure.
Abstract: We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical anti-invariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quarter-symmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.

11 citations

Posted Content
TL;DR: In this paper, it was shown that a light-like hypersurface of a statistical manifold is not a canonical manifold with respect to the induced connections, but the screen distribution has a canonical statistical structure.
Abstract: Lightlike hypersurfaces of a statistical manifold are studied. It is shown that a lightlike hypersurface of a statistical manifold is not a statistical manifold with respect to the induced connections, but the screen distribution has a canonical statistical structure. Some relations between induced geometric objects with respect to dual connections in a lightlike hypersurface of a statistical manifold are obtained. An example is presented. Induced Ricci tensors for lightlike hypersurface of a statistical manifold are computed.

8 citations

Journal ArticleDOI
TL;DR: In this article, the authors study slant submanifolds of Riemannian manifolds with golden structure and provide some non-trivial examples of slant subsets of a manifold with Golden structure.
Abstract: In this paper, we study slant submanifolds of Riemannian manifolds with Golden structure. A Riemannian manifold $(\tilde{M},\tilde{g},{\varphi})$ is called a Golden Riemannian manifold if the $(1,1)$ tensor field ${\varphi}$ on $\tilde{M}$ is a golden structure, that is ${\varphi}^{2}={\varphi}+I$ and the metric $\tilde{g}$ is ${\varphi}-$ compatible. First, we get some new results for submanifolds of a Riemannian manifold with Golden structure. Later we characterize slant submanifolds of a Riemannian manifold with Golden structure and provide some non-trivial examples of slant submanifolds of Golden Riemannian manifolds.

7 citations

Posted Content
TL;DR: In this article, the Chen-Ricci inequality was proved for statistical submanifolds in a statistical manifold of constant φ-sectional curvature, where π is the number of vertices in the manifold.
Abstract: Kenmotsu geometry is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In this article, we study the statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properties of Kenmotsu statistical manifolds. We prove that a Kenmotsu statistical manifold is not a Ricci-flat statistical manifold with an example. Finally, we prove a very well-known Chen-Ricci inequality for statistical submanifolds in Kenmotsu statistical manifolds of constant $\phi-$sectional curvature by adopting optimization techniques on submanifolds. This article ends with some concluding remarks.

4 citations


Cited by
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Book ChapterDOI
01 Oct 2007

131 citations

01 Jan 2007
TL;DR: The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given in this article as a first step of the statistical submanifold theory.
Abstract: The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given as a first step of the statistical submanifold theory. A complex version of the notion of statistical structures is also introduced.

79 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduced light-like hypersurfaces of a golden semi-Riemannian manifold and proved that there is no radical anti-invariant light-based hypersurface of such a manifold.
Abstract: We introduce lightlike hypersurfaces of a golden semi-Riemannian manifold. We investigate several properties of lightlike hypersurfaces of a golden semi-Riemannian manifold. We prove that there is no radical anti-invariant lightlike hypersurface of a golden semi-Riemannian manifold. In particular, we obtain some results for screen semi-invariant lightlike hypersurfaces of a golden semi-Riemannian manifold. Moreover, we study screen conformal screen semi-invariant lightlike hypersurfaces.

32 citations

Posted Content
TL;DR: A minimum description length of a deep learning model is derived, where the spectrum of the Fisher information matrix plays a key role to reduce the model complexity.
Abstract: How do deep neural networks benefit from a very high dimensional parameter space? Their high complexity vs stunning generalization performance forms an intriguing paradox. We took an information-theoretic approach. We find that the locally varying dimensionality of the parameter space can be studied by the discipline of singular semi-Riemannian geometry. We adapt Fisher information to this singular neuromanifold. We use a new prior to interpolate between Jeffreys' prior and the Gaussian prior. We derive a minimum description length of a deep learning model, where the spectrum of the Fisher information matrix plays a key role to reduce the model complexity.

14 citations