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Geometric and Physical Properties of Curvature Tensors -A Review
Journal of International Academy Of Physical Sciences, 2023 Bernard Riemann was the first to define curvature tensor. Most of the curvature tensors are defined with the help of Riemann curvaturetensor, Ricci tensor and metric tensor.It has been observed that different combinations of Ricci tensor and metric ...
G. Pokhariyal
semanticscholar +1 more source
Biharmonic almost complex structures
Forum of Mathematics, Sigma, 2023 This project uses methods in geometric analysis to study almost complex manifolds. We introduce the notion of biharmonic almost complex structure on a compact almost Hermitian manifold and study its regularity and existence in dimension four.
Weiyong He
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On some curves in three-dimensional $$\beta $$ β -Kenmotsu manifolds
Arabian Journal of Mathematics, 2022 This paper is devoted to examine necessary and sufficient conditions for a Frenet curve to be f-harmonic, f-biharmonic, bi-f-harmonic and f-biminimal in three-dimensional $$\beta $$ β -Kenmotsu manifolds. In addition, such conditions are investigated for
Şerife Nur Bozdağ +2 more
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The Adjunction Inequality for Weyl-Harmonic Maps
Complex Manifolds, 2020 In this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical 𝒥-holomorphic curves in the ...
Ream Robert
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A study on magnetic curves in trans-Sasakian manifolds
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper, we focused on biharmonic, f-harmonic and f-biharmonic magnetic curves in trans-Sasakian manifolds. Moreover, we obtain necessary and su cient conditions for magnetic curves as well as Legendre magnetic curves to be biharmonic, f-harmonic ...
Bozdağ Şerife Nur
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Lipschitz minimality of the multiplication maps of unit complex, quaternion and octonion numbers [PDF]
, 2013 We prove that the multiplication maps S n S n ! S n (nD 1;3;7) for unit complex, quaternion and octonion numbers are, up to isometries of domain and range, the unique Lipschitz constant minimizers in their homotopy classes.
Haomin Wen
semanticscholar +1 more source
Some recent progress of biharmonic submanifolds [PDF]
, 2015 In this note, we give a brief survey on some recent developments of biharmonic submanifolds. After reviewing some recent progress on Chen’s biharmonic conjecture, the Generalized Chen’s conjecture on biharmonic submanifolds of non-positively curved ...
Ye-lin Ou
semanticscholar +1 more source
Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds [PDF]
, 2014 We study 4-dimensional Riemannian manifolds equipped with a minimal and conformal foliation $\mathcal F$ of codimension 2. We prove that the two adapted almost Hermitian structures $J_1$ and $J_2$ are both cosymplectic if and only if $\mathcal F$ is ...
Gudmundsson, Sigmundur
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A note on balance equations for doubly periodic minimal surfaces [PDF]
, 2016 Most known examples of doubly periodic minimal surfaces in $\mathbb{R}^3$ with parallel ends limit as a foliation of $\mathbb{R}^3$ by horizontal noded planes, with the location of the nodes satisfying a set of balance equations. Conversely, for each set
Connor, Peter
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Smooth long‐time existence of Harmonic Ricci Flow on surfaces
Journal of the London Mathematical Society, Volume 95, Issue 1, Page 277-304, February 2017., 2017 Abstract We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long‐time existence for the Harmonic Ricci Flow with large coupling constant.
Reto Buzano, Melanie Rupflin
wiley +1 more source