Einstein manifolds are trivial examples of gradient Ricci soli-tons with constant potential function and thus they are called trivial Ricci solitons. In this paper, we prove two characterizations of compact shrinking trivial Ricci solitons.
A slant immersion was introduced in  as an isometric immersion of a Rie-mannian manifold into an almost Hermitian manifold (˜ M , g, J) with constant Wirtinger angle. From J-action point of view, the most natural surfaces in an almost Hermitian manifold are slant surfaces. Flat slant surfaces in complex space forms have been studied in [3, 4]. In this… (More)
A Ricci soliton (M, g, v, λ) on a Riemannian manifold (M, g) is said to have concurrent potential field if its potential field v is a concurrent vector field. In the first part of this paper we classify Ricci solitons with concurrent potential fields. In the second part we derive a necessary and sufficient condition for a submanifold to be a Ricci soliton… (More)
y − x ≥ v(y) − v(x) d − h ≥ b + |M n | 2 − 1 a − 1 ≥ b 2 − 1 a − 1 in this case as well. Again, the unboundedness of D(v, M) follows.