Vol.3, No 14, 2003 pp. 805-819
UDC 514.763.4
Invited Paper

---

ON WEAKLY SYMMETRIC STRUCTURES
ON A RIEMANNIAN MANIFOLD
U. C. De
Department of Mathematics, University of Kalyani, Nadia, West Bengal, India 741235
e-mail: ucde@klyuniv.ernet.in

---

Abstract.  This is a survey article on weakly symmetric structures on a Riemannian manifold.The study of weakly symmetric and weakly projective symmetric Riemannian manifold were initiated byTamassy and Binh. Later on several authors studied weakly symmetric Riemannian manifold and analogous structures, viz. weakly Ricci symmetric, weakly projective symmetric and weakly conformally symmetric Riemannian manifolds. Here we present a brief survey of results on weakly symmetric structures on a Riemannian manifold and some applications in the theory of Relativity.
Key words:  Pseudo symmetric manifold, weakly symmetric manifold, weakly Ricci symmetric manifold, weakly conformally symmetric manifold, weakly projective symmetric manifold.

---

O SLABOSIMETRIČNIM STRUKTURAMA
RIEMANIAN MNOGOSTRUKOSTI U ovom radu je dat pregled o slabosimetričnim strukturama Riemanian mnogostrukosti. Studirane su slabo simetrične i slabo projektivne simetrične Riemannian mnogostrukosti koje su započei Tamassy i Binh. Kasnije jedan broj autora je studirao slabosimetričnu  Riemanian mnogostrukost i nalogne strukture, kao i slabe Riccijeve simetrčne, slabo projektivne simetrične i slabo konformno simetrične Riemannian mnogostrukosti. Ovde, u vom raduje prikazan pregled rezultata o slabosimetričnim strukturama na Riemannian mnogostrukosti i neke primene u teoriji relativnosti.
Ključne reči: Psoudo simetrična mnogostrukost, slabosimetrična mnogostrukost, slabo Ricci-jeva simetrična mnogostrukost, slabo konformna simetrična mnogostrukost, slabo projektivna simetrična mnogostrukost.