bochner formula
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2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Fida El Chami ◽  
Georges Habib

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 287-297
Author(s):  
Gabriel Bercu ◽  
Mircea Crasmareanu

By using the additive and multiplicative separation of variables we find some classes of solutions of the Laplace equation for a generalization of the Poincar? upper half plane metric. Non-constant totally geodesic functions implies the flat metric and several examples are studied including the Hamilton?s cigar Ricci soliton. The Bochner formula is discussed for our generalized Poincar? metric and for its important particular cases.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Akram Ali ◽  
Fatemah Mofarreh ◽  
Wan Ainun Mior Othman ◽  
Dhriti Sundar Patra

AbstractIn the present, we first obtain Chen–Ricci inequality for C-totally real warped product submanifolds in cosymplectic space forms. Then, we focus on characterizing spheres and Euclidean spaces, by using the Bochner formula and a second-order ordinary differential equation with geometric inequalities. We derive the characterization for the base of the warped product via the first eigenvalue of the warping function. Also, it proves that there is an isometry between the base $\mathbb{N}_{1}$ N 1 and the Euclidean sphere $\mathbb{S}^{m_{1}}$ S m 1 under some different extrinsic conditions.


2018 ◽  
Vol 29 (7-8) ◽  
pp. 1135-1139 ◽  
Author(s):  
Mohammed Jamali ◽  
Mohammad Hasan Shahid

2009 ◽  
Vol 92 (4) ◽  
pp. 335-343 ◽  
Author(s):  
Ricardo Abreu-Blaya ◽  
Juan Bory-Reyes

2007 ◽  
Vol 88 (4) ◽  
pp. 358-363 ◽  
Author(s):  
Frank Sommen ◽  
Dixan Peña Peña

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