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Investigating Conformal Vector Field on Riemannian Manifolds

Hessam, Hamed | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44642 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Fanai, Hamid Reza
  7. Abstract:
  8. At first the killing vector fields will be investigated. Conditions are introduced for the hypersurface of a Riemannian manifold with a killing vector field to be equipped with the same killing vector field. Then 2-killing vector field is studied and its relation with killing vector fields and monotone vector fields is presented. After that conformal vector fields are discussed and conditions are introduced in order that the Riemannian manifold equipped with a conformal vector field, isisometric to n-dimensional sphere with constant curvature. Finally we will present the conditions which conformal vector field is a 2-killing vector field. Then we will present the results in which the 2-killing vector field and killing vector field are equivalent and we will specify conditions that 2-killing vector field is a parallel vector field. This research will also describe following papers: Alodan, H.; Hypersurfaces of a Riemannian manifold with killing vector field; Balkan J. Geom. APPL. 13, 2011; P 19-26. Opera, T.; 2-Killing vector fields on Riemannian manifolds; Balkan J. Geom. APPL. 13, 2008; P 87-92. Deshmukh, S.; Conformal vector fields and eigenvectors of laplacian operator; J. Anal.Geom. 15, 2012; P 163-172
  9. Keywords:
  10. Conformal Vector Field ; Killing Vector Field ; 2-Killing Vector Field ; Divergence Operator ; Laplace Operators

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