Acta mathematica scientia, Series B >
GENERIC WARPED PRODUCT SUBMANIFOLDS %OF LOCALLY CONFORMAL KEAHLER MANIFOLDS
Received date: 2008-10-23
Online published: 2010-09-20
Supported by
This work is supported by the research grant (162/428) of the Research centre, faculty of Science, King Abdul Aziz University, K.S.A.
Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star (cf. [9]). The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen's work on CR-warped product submanifolds of Kaehler manifolds (cf. [6], [7]). Later on, similar studies were carried out in the setting of l.c.K. manifolds and nearly Kaehler manifolds (cf. [3], [11]). In the present article, we investigate a larger class of warped product submanifolds of l.c.K. manifolds, ensure their existence by constructing an example of such manifolds and obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we obtain a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold.
Nargis Jamal??20Khalid Ali Khan , Viqar Azam Khan . GENERIC WARPED PRODUCT SUBMANIFOLDS %OF LOCALLY CONFORMAL KEAHLER MANIFOLDS[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1457 -1468 . DOI: S0252-9602(10)60138-5
[1] Bishop R L, O'Neill. Manifolds of negative curvature. Trans Amer Math Soc, 1969, 145: 1--49
[2] Blair D E, Dragomir. CR-products in locally conformal Kaehler manifolds. Kyushu J Math, 2001, 55: 337--362
[3] Bonanzinga V, Matsumoto K. Warped product CR-submanifolds in locally conformal Kaehler manifolds. Periodica Math Hungarica, 2004, 48: 207--221
[4] Chen B Y. CR-submanifolds of a Kaehler manifold I. J Diff Geom, 1981, 16: 305--322 and 493--509
[5] Chen B Y. Differential geometry of real submanifolds in Kaehler manifold. Monatsh Math, 1981, 91: 257--274
[6] Chen B Y. Geometry of warped product CR-submanifolds in Kaehler manifolds I. Monatsh Math, 2001, 133: 177--195
[7] Chen B Y. Geometry of warped product CR-submanifolds in Kaehler manifolds II. Monatsh Math, 2001, 134: 103--119
[8] Hasan S, Husain S I. Generic submanifolds of locally conformal Kaehler manifolds. Soochow J Math, 1988, 14: 111--117
[9] Hong S T. Warped products and black holes. Nuovo Cim J B, 2005, 120: 1227--1234
[10] Hiepko S. Eine Inner Kennzeichungder verzerrten Produkte. Math Ann, 1979, 241: 209--215
[11] Khan V A, Khan K A, Sirajuddin. Warped product CR-submanifolds in nearly Kaehler manifolds. SUT J Math, 2007, 43: 201--213
[12] Matsumoto K. On CR-submanifolds of locally conformal Kaehler manifolds. J. Korean Math Soc, 1984, 21: 49--61 and tensor (N.S) 1987, 45: 144--150
[13] Nolker S. Isometric Immersions of warped product. Differential Geom Appl, 1996, 6: 1--30
[14] Papaghiuc N. Semi-slant submanifolds of Kaehler manifold. An St Univ AI I Cuza Iasi, 1994, 40: 55--61
[15] Sahin B. Non-existence of warped product semi-slant submanifolds of Kaehler manifold. Geom Dedicata, 2006, 117: 195--202
[16] Vaisman I. Locally conformal almost Kaehler manifolds. Israel J Math, 1976, 24: 338--351
[17] Vaisman I. On locally and globally conformal Kaehler manifolds. Trans Amer Math Soc, 1980, 262: 533--534
/
| 〈 |
|
〉 |