Abstract

 
 
 In this paper we state and prove a characteristic relation which exists, between the eigenspaces of the Ricci transformation $R(N, - )N$ acting on the orthocomplement space of $N$ in $T_mM$ where $m \in M$, $M$ being a locally symmetric space, and the Weingarten map $S_N$ of small enough geodesic tubes of $M$. 
 
 
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