ðàáîòå ïðèâîäèòñÿ ôîðóëà äëÿ ðåøåíèÿ îäíîðîäíîãî âîëíîâîãî óðàâíåíèÿ íà ðèìàíîâîì ìíîãîîáðàçèèD çàäàííàÿ ñ ïîìîùüþ îïåE ðàòîðà ñôåðè÷åñêîãî ñðåäíåãîD ïðèìåíÿåìîãî ê íà÷àëüíûì äàíE íûìF Êëþ÷åâûå ñëîâàX âîëíîâîå óðàâíåíèåD äèôôåðåíöèàëüíûå óðàâíåE íèÿD îïåðàòîð ñôåðè÷åñêîãî ñðåäíåãîF Wave equation on a Riemannian manifold and the Spherical mean operator We give a formula for the solution to the homogeneous wave equation on a Riemannian manifold in terms of Spherical mean operator which is being applied to initial data.