Geodesic
CHARACTERIZATIONS OF RICCI FLAT METRICS AND LAGRANGIAN SUBMANIFOLDS IN TERMS OF THE VARIATIONAL PROBLEM
Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 643-651

Voir la notice de l'article provenant de la source Cambridge University Press

Given the pair (P, η) of (0,2) tensors, where η defines a volume element, we consider a new variational problem varying η only. We then have Einstein metrics and slant immersions as critical points of the 1st variation. We may characterize Ricci flat metrics and Lagrangian submanifolds as stable critical points of our variational problem. 
TANIGUCHI, TETSUYA; UDAGAWA, SEIICHI. CHARACTERIZATIONS OF RICCI FLAT METRICS AND LAGRANGIAN SUBMANIFOLDS IN TERMS OF THE VARIATIONAL PROBLEM. Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 643-651. doi: 10.1017/S0017089514000536
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     title = {CHARACTERIZATIONS {OF} {RICCI} {FLAT} {METRICS} {AND} {LAGRANGIAN} {SUBMANIFOLDS} {IN} {TERMS} {OF} {THE} {VARIATIONAL} {PROBLEM}},
     journal = {Glasgow mathematical journal},
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     doi = {10.1017/S0017089514000536},
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