Browse > Article
http://dx.doi.org/10.5831/HMJ.2022.44.1.62

A NEW TYPE WARPED PRODUCT METRIC IN CONTACT GEOMETRY  

Mollaogullari, Ahmet (Department of Mathematics, Faculty of Arts and Sciences, Canakkale Onsekiz Mart University)
Camci, Cetin (Department of Mathematics, Faculty of Arts and Sciences, Canakkale Onsekiz Mart University)
Publication Information
Honam Mathematical Journal / v.44, no.1, 2022 , pp. 62-77 More about this Journal
Abstract
This study presents an 𝛼-Sasakian structure on the product manifold M1 × 𝛽(I), where M1 is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.
Keywords
almost contact manifolds; Sasaki manifolds; Kahler Manifolds; warped product;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 D.E. Blair and J.A. Oubina, Conformal and related changes of metric on the product of two almost contact metric manifolds, Publicacions Matematiques 34 (1990), 199-207.   DOI
2 N. Aktan, G. Ayar, and I. Bektas, A Schur type theorem for almost cosymplectic manifolds with Kahlerian leaves, Hacettepe Journal of Mathematics and Statistics (42) (2013), no. 4, 455-463.
3 P. Alegre and A. Carriazo, Generalized sasakian space forms and conformal Cchanges of the metric, Results. Math. 59 (2011), 485--493.   DOI
4 K. Arslan, R. Ezentas, I. Mihai, and C. Murathan,Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc. 42 (2005), no. 5, 1101-1110.   DOI
5 M. Atceken, Contact CR-warped product sunmanifolds in cosymlectic space forms, Collect. Math. 62 (2011), 1726-1741.   DOI
6 D.E. Blair, Contact Manifolds in Riemannian Geometry, Springer, Berlin, Heidelberg, 1976.
7 D.E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, Boston, 2010.
8 D.E. Blair, D-homothetic warping. Publications De L'institut Mathematique 94 (2013), no. 108, 47-54.   DOI
9 M. Caprusi, Some remarks on the product of two almost contact manifolds, Al. I.Cuza XXX (1984), 75-79.
10 B.Y. Chen, Diferantial Geometry of Warped Product Manifolds and Submanifolds, World Scientific, Singapore, 2017.
11 B. Gherici, A.M. Cherif, and K. Zegga, Sasakian structures on products of real line and Kahlerian manifold, The Korean Journal of Mahematics 27 (2019), no. 4, 1061-1075.
12 H. Gieges, A brief history of contact geometry and topology, Expositiones Mathematicae 19 (2001), 25-53.   DOI
13 K. Matsumoto and I. Mihai, Warped product submanifolds in Sasakian space forms, SUT J. Math. 38 (2002), 135-144.
14 S. Sular and C. Ozgur, Doubly warped product submanifolds of (k,µ)-contact metric manifolds, Ann. Polon. Math. 100 (2011), no. i, 223-236.   DOI
15 K. Yano and M. Kon, Structures on Manifolds, World Scientific, 1984.
16 K. Zegga, B. Gherici, and A.M. Cherif, Sasakian structure on the product of Sasakian and Kahlerian manifolds, Journal of Geometry and Topology 20 (2017), no. 4, 409-425   DOI
17 H.B. Pandey, Cartesian product of two manifolds, Indian J. Pure Appl. Math. 12 (1981), no. 1, 55-60.