… a geodesic. The connection between the existence of closed geodesics and monotone vector
fields will … geodesics and geodesic monotone vector fields. It is easy to prove the following …

… We define the notion of geodesic monotone vector fields on Riemannian manifolds. This …
∗, then the geodesic monotone vector fields on B can be identified with the monotone operators …

… that the square of such a vector field's norm is a coercive map. In … monotone vector fields,
showing that if there exists a strictly monotone vector field then there exists no closed geodesic …

… The concept of strong monotonicity of such fields was introduced in [3]. We introduce the
concept of point-to-set monotone vector field … If c itself is parallel we say that c is a geodesic. The …

… class of maximal monotone vector fields coincides with the class of vector fields that are
upper… If γ itself is parallel along γ, then we say that γ is a geodesic, and in this case c is constant. …

… monotone point-to-set maps in [2] and in [9]. In this work we recall the concept of monotone
vector fields in … The restriction of a geodesic to a closed bounded interval is called a geodesic …

… monotone vector fields, which previously have been introduced in the framework of Riemannian
manifolds, as well as the notion of accretive vector field … that γ is a geodesic (this notion …

… ) if and only if the first variation of the length of every geodesic arc γ with infinitesimal … of
geodesic monotone vector fields, we prove that there is no strictly geodesic monotone vector field …

… monotone vector fields and firmly nonexpansive mappings is established. This fact is then
used to prove that the resolvent of a maximal monotone vector field … that γ is a geodesic, and in …

… In the present paper, we study geodesic mappings of … of geodesic mappings on V n ( K )
-spaces forms a special Jordan algebra and the set of solutions generated by concircular fields …