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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 74 Issue: 1

Fischer-Marsden conjecture on K-paracontact manifolds and quasi-para-Sasakian manifolds

Mustafa Özkan(BURSA TECHNICAL UNIVERSITY)0000-0002-4483-2912
İrem Küpeli Erken(Bursa Technical University)0000-0003-4471-3291
Sayfa
—
Yayın Tarihi
2025-03-08
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The second one is the manifold is paracosymplectic manifold and η-Einstein.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The aim of this paper is to study of the non-trivial solutions of Fischer-Marsden conjecture on K-paracontact manifolds and 3-dimensional quasi-para-Sasakian manifolds.
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Temel Bulgular & Veri:We prove that if a semi-Riemannian manifold of dimension $2n+1$ admits a non-trivial solution of Fischer-Marsden equation, then it has constant scalar curvature.
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Sonuç & Katkı:The second one is the manifold is paracosymplectic manifold and η-Einstein.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fischer-Marsden equation · K-paracontact manifold · quasi-para-Sasakian manifold

Abstract

The aim of this paper is to study of the non-trivial solutions of Fischer-Marsden conjecture on K-paracontact manifolds and 3-dimensional quasi-para-Sasakian manifolds. We prove that if a semi-Riemannian manifold of dimension $2n+1$ admits a non-trivial solution of Fischer-Marsden equation, then it has constant scalar curvature. We give a comprehensive classification for a $(2n+1)$-dimensional K-paracontact manifold which admits a non-trivial solution of Fischer-Marsden equation. We consider 3-dimensional quasi-para-Sasakian manifolds with $\beta$ constant which admits Fischer-Marsden equation and prove that there are two possibilities. The first one is the scalar curvature $r = −6\beta^2$ and $M^3$ is Einstein. The second one is the manifold is paracosymplectic manifold and η-Einstein.

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Bu Makaleye Atıf Yap

Özkan, M., Erken, İ. K. (2025). Fischer-Marsden conjecture on K-paracontact manifolds and quasi-para-Sasakian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 74 Issue: 1. https://doi.org/10.31801/cfsuasmas.1485231

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