The set of Eulerian subgraphs of some undirected graph G together with the geographic differences of edges forms a vector space over GF(2). Its bases have been intensively studied and various kinds like minimal length, fundamental or robust cycle bases that entirely consists of (geodetically) convex elementary cycles, i.e., that contain all shortest path between any two vertices of theses cycles. In particular we investigate convex cycle bases in isometric subgraphs of Cartesian products.