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RISS 인기검색어
- 검색키워드
- 저자 : Behroz Bidabad (검색결과 6 건)
- 무료
- 기관 내 무료
- 유료
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ON EVOLUTION OF FINSLER RICCI SCALAR
Bidabad, Behroz,Sedaghat, Maral Khadem Korean Mathematical Society 2018 대한수학회지 Vol.55 No.3
Here, we calculate the evolution equation of the reduced hh-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced hh-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.
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On evolution of Finsler Ricci scalar
Behroz Bidabad,Maral Khadem Sedaghat 대한수학회 2018 대한수학회지 Vol.55 No.3
Here, we calculate the evolution equation of the reduced $hh$-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced $hh$-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.
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THE SCHWARZIAN DERIVATIVE AND CONFORMAL TRANSFORMATION ON FINSLER MANIFOLDS
Bidabad, Behroz,Sedighi, Faranak Korean Mathematical Society 2020 대한수학회지 Vol.57 No.4
Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere S<sup>n-1</sup> in ℝ<sup>n</sup>. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.
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The Schwarzian derivative and conformal transformation on Finsler manifolds
Behroz Bidabad,Faranak Sedighi 대한수학회 2020 대한수학회지 Vol.57 No.4
Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere $ S^{n-1}$ in $ \mathbb{R}^n $. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.
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DEFORMATION OF CARTAN CURVATURE ON FINSLER MANIFOLDS
Bidabad, Behroz,Shahi, Alireza,Ahmadi, Mohamad Yar Korean Mathematical Society 2017 대한수학회보 Vol.54 No.6
Here, certain Ricci flow for Finsler n-manifolds is considered and deformation of Cartan hh-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.
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Deformation of Cartan curvature on Finsler manifolds
Behroz Bidabad,Alireza Shahi,Mohamad Yar Ahmadi 대한수학회 2017 대한수학회보 Vol.54 No.6
Here, certain Ricci flow for Finsler $n$-manifolds is considered and deformation of Cartan $hh$-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.
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