Reconstruction of an Affine Connection in Generalized Fermi Coordinates

Geodesic Vector Fields on a Riemannian Manifold

“…Physically, a geodesic vector field has integral curves with an acceleration vector always proportional to the velocity vector. These fields are connected with generalized Fermi coordinates [1]. Geodesic vector fields naturally appear in many situations as seen in the following examples:…”

“…Consider unit hypersphere S n in the Euclidean space (R n+1 , , ). Then, the restriction of coordinate vector field ∂ ∂u 1 on R n+1 to S n can be expressed as…”

“…where ρ = ∂ ∂u 1 , N , N being unit normal to S n and ξ is vector field on S n , which is the tangential component of ∂ ∂u 1 . Then it is easy to see that on S n , we have ∇ ξ ξ = ρξ, that is, ξ is a geodesic vector field on S n .…”

“…Similarly, special vector fields such as unit geodesic vector fields, Killing vector fields, concircular vector fields, conformal vector fields are used in studying geometry as well as topology of a Riemannian manifold (cf. [1][2][3][4][6][7][8][9][10][11][16][17][18][19][20][21][22][23][24][25][26][27][28][29]).…”

О Предписанных Значениях Оператора Секционной Кривизны На Трехмерных Локально Однородных Лоренцевых Многообразиях

“…[1,2]). Некоторые результаты о восстановлении (псевдо)римановых метрик и аффинных связностей по заданному тензору кривизны содержится в статье Й. Микеша и А. Ванжуровой [12], а также в монографии [11].…”