JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A CURVATURE-LIKE TENSOR FIELD ON A SASAKIAN MANIFOLD
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A CURVATURE-LIKE TENSOR FIELD ON A SASAKIAN MANIFOLD
Kim, Young-Mi;
  PDF(new window)
 Abstract
We investigate a curvature-like tensor defined by (3.1) in Sasakian manifold of 5, and show that this tensor satisfies some properties. Especially, we determine compact Sasakian manifolds with vanishing this tensor and improve some theorems concerning contact conformal curvature tensor and spectrum of Laplacian acting on on the manifold by using this tensor component.
 Keywords
Sasakian manifold;curvature-like tensor field;D-homothetic;spectrum;
 Language
English
 Cited by
 References
1.
M. Berger, P. Gauduchonm, and E. Mazet, Le Spectre d'une Variete riemanni- enne, Lecture Notes in Mathematics 194, Springer-Verlag, 1971

2.
W. M. Boothby and H. C. Wang, On contact manifolds, Ann. of Math (2) 68 (1958), 721-734 crossref(new window)

3.
S. Funabashi, H. S. Kim, Y. -M. Kim, and J. S. Pak, Traceless component of the conformal curvature tensor in Kahler manifold, preprint

4.
J. C. Jeong, J. D. Lee, G. H. Oh, and J. S. Pak, On the contact conformal curvature tensor, Bull. Korean Math. Soc. 27 (1990), no. 2, 133-142

5.
M. Matsumoto and G. chuman, On the C-Bochner curvature tensor, TRU Math. 5 (1969), 21-30

6.
K. Ogiue, On almost contact manifolds admitting axiom of planes or axioms of free mobility, Kodai Math. Sem. Rep 16 (1964), 223-232

7.
J. S. Pak, J. C. Jeong, and W. -T. Kim, The contact conformal curvature tensor field and the spectrum of the Laplacian, J. Korean Math. Soc. 28 (1991), no. 2, 267-274

8.
V. K. Patodi, Curvature and the fundamental solution of the heat operator, J. Indian Math. Soc. 34 (1970), no. 3-4, 269-285

9.
S. Sasaki, Almost contact manifolds, Lecture Notes I, II, Tohoku Univ, 1965

10.
S. Tanno, Sasakian manifolds with constant $\phi$-holomorphic sectional curvature, Tohoku Math. J. (2) 21 (1969), 501-507 crossref(new window)

11.
S. Tanno, Eigenvalues of the Laplacian of Riemannian manifolds, Tohoku Math. J. 25 (1973), 391-403 crossref(new window)

12.
Gr. Tsagas, On the spectrum of the Laplace operator for the exterior 2-forms, Tensor (N. S.) 33 (1979), no. 1, 94-96

13.
S. Yamaguchi and G. Chuman, Eigenvalues of the Laplacian of Sasakian man- ifolds, TRU Math. 15 (1979), no. 2, 31-41