| dc.description.abstract | This thesis is the key to good understanding of di erential geometry with
para- Kenmotsu and Lorentzian Para- Sasakian structure and it is organized
as follows. In chapter one, the preliminaries and de nitions are introduced,
where, Manifolds, di erentiable structures, Riemannian Manifolds and
Ricci
ows are de ned. In chapter two the relevant literature is reviewed and
Propositions and theorems proved in area are included. In chapter three,
Ricci solitons on para- Kenmotsu Manifolds satisfying ( ; :)s:W8 = 0 and
( ; :)W8:S = 0 are discussed and we have proved that the Para- Kenmotsu
manifolds satisfying ( ; :)W8:S = 0: are quasi- Einstein Manifolds and those
satisfying ( ; :)S:W8 = 0; are Einstein Manifolds.Also it has been proved
that the para- Kenmotsu manifolds with cyclic Ricci tensor and Ricci
soliton structure are quasi-Einstein manifolds . In chapter four, Ricci solitons
on Lorentzian Para- Sasakian manifolds satisfying ( ; :)s:W8 = 0 and
( ; :)W8:S = 0 are treated and it has been proved that Lorentzian Para-
Sasakian manifolds satisfying ( ; :)s:W8 = 0 and having Ricci soliton
structure are quasi-Einstein manifolds and those satisfying ( ; :)W8:S = 0 are
Einstein manifolds. In chapter ve, we discuss Ricci solitons on Lorentzian
Para- Sasakian manifolds satisfying ( ; :)s:W2 = 0 and ( ; :)W2:S = 0 and it
was found that, Lorentzian Para- Sasakian manifolds satisfying ( ; :)s:W2 = 0
and having Ricci soliton structure are Einstein or quasi-Einstein manifolds
according to the value of and : In Chapter six, results are discussed
and the connection between Ricci solitons and Einstein metrics on Para-
Kenmotsu and Lorentzian Para Sasakian Manifolds has been established. | en_US |
