Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Vertical Generalized Berger-type Metrics: A New Perspective on Harmonic Vector Fields
Authors: Abderrahim Zagane, Aydin Gezer, Saadia Chaoui
Keywords: Anti-paraK\"{a}hler manifold, tangent bundle, vertical generalized Berger-type deformed Sasaki metric, harmonic maps
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Keywords: Anti-paraK\"{a}hler manifold, tangent bundle, vertical generalized Berger-type deformed Sasaki metric, harmonic maps
Abstract
In this paper, we introduce a metric called the vertical generalized Berger-type deformed Sasaki metric, defined on the tangent bundle of an anti-paraK\"{a}hler manifold. First, we analyze the harmonicity of vector fields with respect to this new metric, providing examples that illustrate how certain vector fields satisfy the harmonicity condition under the introduced metric. These examples demonstrate the unique properties and behavior of harmonic vector fields on anti-paraK\"{a}hler manifolds equipped with this specific metric. Next, we explore the harmonicity of a vector field along a map between Riemannian manifolds, where the target manifold is anti-paraK\"{a}hler and its tangent bundle is equipped with the vertical generalized Berger-type deformed Sasaki metric. Finally, we investigate the harmonicity of the composition of two specific maps. The first map is the projection from the tangent bundle of a Riemannian manifold (the source manifold) onto the manifold itself, and the second map is from this Riemannian manifold to another Riemannian manifold. The source manifold is an anti-paraK\"{a}hler manifold, and its tangent bundle is endowed with the vertical generalized Berger-type deformed Sasaki metric. We discuss the conditions under which the composition of these maps produces harmonic vector fields.Abderrahim Zagane, Saadia Chaoui
Relizane University, Department of Mathematics, Faculty
of Science and Technology, 48000, Relizane-Algeria
E-mail:
Aydin Gezer
Ataturk University, Department of Mathematics, Faculty
of Science, 25240, Erzurum-T¨urkiye.
E-mail:
Relizane University, Department of Mathematics, Faculty
of Science and Technology, 48000, Relizane-Algeria
E-mail:
Aydin Gezer
Ataturk University, Department of Mathematics, Faculty
of Science, 25240, Erzurum-T¨urkiye.
E-mail:
DOI
https://doi.org/10.56415/basm.y2025.i1.p58Fulltext
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Contents
- Generalized Berezin transform and Schatten class operators on weighted Bergman spaces
- Reverse Hardy inequalities via μ-proportional generalized fractional integral operators
- Some integrals for cosine families of bounded linear operators on some non-Archimedean Banach spaces
- About the Laplace transform on ${{L}^{1}}\left( \mathbb{R^+} \right)$
- Vertical Generalized Berger-type Metrics: A New Perspective on Harmonic Vector Fields
- On conharmonic curvature tensor of 6-dimensional planar Hermitian submanifolds of Cayley algebra
- Completeness of the factor group of a complete topological group and completeness of the factor ring of a complete topological ring by a compact normal subgroup and a compact ideal, respectively.
- Pure and Mixed Stationary Equilibria for Dynamic Positional Games on Graphs
- On 4-T-quasigroups with exactly 20 distinct parastrophes
