Geodesic
K\"ahler geometry of the infinite-dimensional homogeneous space $M=\operatorname{Diff}_+(S^1)/\operatorname{Rot}(S^1)$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 21 (1987) no. 4, pp. 35-46.

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     title = {K\"ahler geometry of the infinite-dimensional homogeneous space $M=\operatorname{Diff}_+(S^1)/\operatorname{Rot}(S^1)$},
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A. A. Kirillov; D. V. Yur'ev. K\"ahler geometry of the infinite-dimensional homogeneous space $M=\operatorname{Diff}_+(S^1)/\operatorname{Rot}(S^1)$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 21 (1987) no. 4, pp. 35-46. http://geodesic.mathdoc.fr/item/FAA_1987_21_4_a2/

[1] Bowick M.J., Rajeev S.G., “String theory as the Kahler geometry of loop space”, Physical Review Letters, 58:6 (1987), 535–538 | DOI | MR

[2] Pilch K., Warner N.P., Holomorphic structure of superstring vacua, Preprint CTP, no. 1457, 1987 | MR | Zbl

[3] Mickelsson J., String quantisation on group manifolds and the holomorphic geometry of Diff $S^1/S^1$, Preprint CTP, no. 1448, 1987 | MR

[4] Bowick M.J., Rajeev S.G., The holomorphic geometry of closed bosonic string theory and Diff $S^1/S^1$, Preprint CTP, no. 1456, 1987 | MR

[5] Kirillov A.A., Yurev D.V., “Kelerova geometriya beskonechnomernogo odnorodnogo mnogoobraziya $M=\operatorname{Diff}_+S^1/\operatorname{Rot}S^1$”, Funktsion. analiz i ego pril., 20:4 (1986), 79–80 | MR | Zbl

[6] Gelfand I.M., Fuks D.B., “Kogomologii algebry Li vektornykh polei na okruzhnosti”, Funktsion. analiz i ego pril., 2:4 (1968), 92–93 | MR

[7] Bott R., “On the characteristic classes of groups of diffeomorphisms”, Enseign. Math., 23:3–4 (1977), 209–220 | MR | Zbl

[8] Neretin Yu.A., “O kompleksnoi polugruppe, soderzhaschei gruppu diffeomorfizmov okruzhnosti”, Funktsion. analiz i ego pril., 21:2 (1987), 82–83 | MR | Zbl

[9] Khart N., Geometricheskoe kvantovanie v deistvii, Mir, M., 1985 | MR

[10] Dubrovin B.A., Krichever I.M., Novikov S.P., “Integriruemye sistemy. I”, Sovremennye problemy matematiki. Fundamentalnye napravleniya, 4, 1985, 179–284 | MR | Zbl

[11] Kirillov A.A., “Infinite-dimensional Lie groups: their orbits, invariants and representations. The geometry of moments”, Lect. Notes in Math., no. 970, 1982, 101–123 | DOI | MR | Zbl

[12] Segal G., “Unitary representations of some infinite dimensional groups”, Comm Math. Phys., 80:3 (1981), 301–342 | DOI | MR | Zbl

[13] de Branges L., “A proof of the Bieberbach conjecture”, Acta Math., 154 (1985), 137–152 | DOI | MR | Zbl

[14] Kirillov A.A., Golenischeva-Kutuzova M.I., Geometriya momentov grupp diffeomorfizmov, Preprint IPM AN SSSR, no. 101, 1986 | MR

[15] Kirillov A.A., “Kelerova struktura na $K$-orbitakh gruppy diffeomorfizmov okruzhnosti”, Funktsion. analiz i ego pril., 21:2 (1987), 42–45 | MR | Zbl

[16] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, Ch. 2, Nauka, M., 1981 | MR