International Journal of Pure and Applied Mathematics Volume 94 No. 3 2014, 403-417 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v94i3.8 P A ijpam.eu ON CR-SUBMANIFOLDS OF (ǫ)-PARACONTACT SASAKIAN MANIFOLD Barnali Laha 1 § , Arindam Bhattacharyya 2 1,2 Department of Mathematics Jadavpur University Kolkata, INDIA Abstract: The object of this paper is to prove some of the properties of (ǫ)- paracontact Sasakian manifold. This paper is summarized as follows: Section (1) is introductory. In Section (2) we sketch the notion of (ǫ)-paracontact metric manifold and (ǫ)-paracontact Sasakian manifold. Section (3) and (4) deals with some properties like D-totally, D ⊥ -totally, mixed totally geodesic etc. CR-submanifold of an (ǫ)-paracontact Sasakian manifold. Section (5) and (6) gives some idea of geometry of leaves and contact CR-product . Finally we have given an example of (ǫ)-paracontact Sasakian manifold. AMS Subject Classification: 53C25, 53C50 Key Words: (ǫ)-paracontact Sasakian manifold, D(D ⊥ )-totally geodesic, mixed totally geodesic, contact CR-product 1. Introduction An almost paracontact structure (φ,ξ,η) satisfying φ 2 = I − η ⊗ ξ and η(ξ )=1 on a differentiable manifold was introduced by Sato [7] in 1976. This structure is analogous to almost contact structure ([6], [14]) and is very much related Received: February 27, 2014 c  2014 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author