Devoted to the study on the theory of H-connected space,which has been investigated by Jungck [1] in detail,we first give Jungck’s theorem another proof free from Whyburn [2] ,and then give another theorem in which“compact”hypothesis in Jungck’s theorem is replaced by the locally connected one.

It is proved that if G is conected, locally connected graph on at least three vertices such that the set of claw centers is independent, and if the subgraph induced by the neighbor of v is strong 2-dominated for any claw centre v , then G is fully cycle extendable.

In this paper, we prove that if G is connected, locally connected graph on at least three vertices such that the set of claw centres B is independent, and if G-B is locally connected, then G is fully cycle extendable.

This paper main studies the qualities of locally dual flat metrics.

It is obtained that the sufficient and necessary conditions of the dual flat Randers metrics whenαis locally projectively flat.

This paper studies the Schouten tensor on the locally conformally flat manifold,and gets some sufficient conditions for M to be the space of constant curvature,which improves the known results.