CRITICALITY OF CHARACTERISTIC VECTOR FIELDS ON ALMOST COSYMPLECTIC MANIFOLDS

Title & Authors
CRITICALITY OF CHARACTERISTIC VECTOR FIELDS ON ALMOST COSYMPLECTIC MANIFOLDS
Pak, Hong-Kyun; Kim, Tae-Wan;

Abstract
Main interest of the present paper is to investigate the criticality of characteristic vector fields on almost cosymplectic manifolds. Killing critical characteristic vector fields are absolute minima. This paper contains some examples of non-Killing critical characteristic vector fields.
Keywords
critical unit vector field;harmonic map;$\small{\phi}$-holomorphic map;almost cosymplectic manifold;Sasaki metric;
Language
English
Cited by
1.
Almost f-Cosymplectic Manifolds, Mediterranean Journal of Mathematics, 2014, 11, 2, 775
References
1.
D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Matnematlcs, Vol. 509. Springer-Verlag, Berlin-New York, 1976

2.
F. G. B. Brito, Total bending of flows with mean curvature correction, Differential Geom. Appl. 12 (2000), no. 2, 157-163

3.
D. Chinea and C. Gonzales, An example of an almost co symplectic homogeneous manifold, Differential geometry, Peniscola 1985, 133-142, Lecture Notes in Math., 1209, Springer, Berlin, 1986

4.
D. Chinea, M. de Leon, and J. C. Marrero, Coeffective cohomology on almost cosymplectic manifolds, Bull. Sci. Math. 119 (1995), no. 1, 3-20

5.
L. A. Cordero, M. Fernandez, and M. De Leon, Examples of compact almost contact manifolds admitting neither Sasakian nor co symplectic structures, Atti Sem. Mat. Fis. Univ. Modena 34 (1985/86), no. 1, 43-54

6.
P. Dacho, On almost cosymplectic manifolds with the structure vector field - belonging to the k-nullity distribution, Balkan J. Geom. Appl. 5 (2000), no. 2, 47-60

7.
P. Dacho and Z. Olszak, On conformally flat almost co symplectic manifolds with Kiihlerian leaves, Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 1, 89-103

8.
P. Dombrowski, On the geometry of the tangent bundles, J. Reine Angew. Math. 210 (1962), 73-88

9.
J. Eells and L. Lemaire, Selected topics in harmonic maps, CBMS Regional Conference Series in Mathematics, 50. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1983

10.
O. Gil-Medrano, Relationship between volume and energy of vector fields, Differential Geom. Appl. 15 (2001), no. 2, 137-152

11.
O. Gil-Medrano and E. Llinares-Fuster, Minimal unit vector fields, Tohoku Math. J. (2) 54 (2002), no. 1, 71-84

12.
H. Gluck and W. Ziller, On the volume of a unit vector field on the three sphere, Comment. Math. Helv. 61 (1986), no. 2, 177-192

13.
S. I. Goldberg and K. Yano, Integrability of almost cosymplectic structures, Pacific J. Math. 31 (1969), 373-382

14.
S. S. Ianus and A. M. Pastore, Harmonic maps on contact metric manifolds, Ann. Math. Blaise Pascal 2 (1995), no. 2, 43-53

15.
D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J. 4 (1981), no. 1, 1-27

16.
K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. (2) 24 (1972), 93-103

17.
Z. Olszak, On almost cosymplectic manifolds, Kodai Math. J. 4 (1981), no. 2, 239-250

18.
Z. Olszak, On almost cosymplectic manifolds with Kiihlerian leaves, Tensor (N. S.) 46 (1987), 117-124

19.
K. Oshikiri, A remark on minimal foliations, Tohoku Math. J. (2) 33 (1981), no. 1, 133-137

20.
H. K. Pak and T. W. Kim, Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 4, 841-846

21.
G. Pitis, Foliations and submanifolds of a class of contact manifolds, C. R. Acad. Sci. Paris Ser. I Math. 310 (1990), no. 4, 197-202

22.
P. Rukimbira, Criticality of K-contact vector fields, J. Geom. Phys. 40 (2002), no. 3-4, 209-214

23.
Ph. Tondeur, Foliations on Riemannian manifolds, Universitext. Springer-Verlag, New York, 1988

24.
C. M. Wood, On the energy of a unit vector field, Geom. Dedicata 64 (1997), no. 3, 319-330

25.
K. Yano and S. Ishihara, Tangent and cotangent bundles: differential geometry, Pure and Applied Mathematics, No. 16. Marcel Dekker, Inc., New York, 1973