Geometry & Topology Volume 15, issue 4 (2011)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Hodge theory on nearly Kähler manifolds

Misha Verbitsky

Geometry & Topology 15 (2011) 2111–2133

DOI: 10.2140/gt.2011.15.2111

Bibliography

1	B S Acharya, J M Figueroa-O’Farrill, C M Hull, B Spence, Branes at conical singularities and holography, Adv. Theor. Math. Phys. 2 (1998) MR1693624
2	B S Acharya, E Witten, Chiral fermions from manifolds of $G_2$ holonomy arXiv:hep-th/0109152
3	M Atiyah, E Witten, $M$–theory dynamics on a manifold of $G_2$ holonomy, Adv. Theor. Math. Phys. 6 (2002) 1 MR1992874
4	C Bär, Real Killing spinors and holonomy, Comm. Math. Phys. 154 (1993) 509 MR1224089
5	H Baum, T Friedrich, R Grunewald, I Kath, Twistors and Killing spinors on Riemannian manifolds, Teubner-Texte zur Math. 124, Teubner Verlag (1991) 180 MR1164864
6	J B Butruille, Classification des variétés approximativement kähleriennes homogènes, Ann. Global Anal. Geom. 27 (2005) 201 MR2158165
7	R Cleyton, A Swann, Einstein metrics via intrinsic or parallel torsion, Math. Z. 247 (2004) 513 MR2114426
8	J Eells, S Salamon, Twistorial construction of harmonic maps of surfaces into four-manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. $(4)$ 12 (1985) MR848842
9	T Friedrich, Nearly Kähler and nearly parallel $G_2$–structures on spheres, Arch. Math. $($Brno$)$ 42 (2006) 241 MR2322410
10	T Friedrich, S Ivanov, Parallel spinors and connections with skew-symmetric torsion in string theory, Asian J. Math. 6 (2002) 303 MR1928632
11	A Gray, Minimal varieties and almost Hermitian submanifolds, Michigan Math. J. 12 (1965) 273 MR0184185
12	A Gray, Nearly Kähler manifolds, J. Differential Geometry 4 (1970) 283 MR0267502
13	A Gray, Weak holonomy groups, Math. Z. 123 (1971) 290 MR0293537
14	A Gray, The structure of nearly Kähler manifolds, Math. Ann. 223 (1976) 233 MR0417965
15	P Griffiths, J Harris, Principles of algebraic geometry, Pure and Applied Math., Wiley-Interscience (1978) MR507725
16	N Hitchin, Stable forms and special metrics, from: "Global differential geometry: the mathematical legacy of Alfred Gray (Bilbao, 2000)" (editors M Fernández, J A Wolf), Contemp. Math. 288, Amer. Math. Soc. (2001) 70 MR1871001
17	S Ivanov, Connections with torsion, parallel spinors and geometry of $\mathrm{{S}pin}(7)$ manifolds, Math. Res. Lett. 11 (2004) 171 MR2067465
18	T Kawasaki, The signature theorem for $V$–manifolds, Topology 17 (1978) 75 MR0474432
19	T Kawasaki, The Riemann–Roch theorem for complex $V$–manifolds, Osaka J. Math. 16 (1979) 151 MR527023
20	T Kawasaki, The index of elliptic operators over $V$–manifolds, Nagoya Math. J. 84 (1981) 135 MR641150
21	V F Kiričenko, $K$–spaces of maximal rank, Mat. Zametki 22 (1977) 465 MR0474103
22	S Kobayashi, K Nomizu, Foundations of differential geometry, Vol. II, Interscience Tracts in Pure and Applied Math. 15, Wiley-Interscience (1969) MR0238225
23	A Moroianu, P A Nagy, U Semmelmann, Unit Killing vector fields on nearly Kähler manifolds, Internat. J. Math. 16 (2005) 281 MR2130627
24	A Moroianu, P A Nagy, U Semmelmann, Deformations of nearly Kähler structures, Pacific J. Math. 235 (2008) 57 MR2379770
25	O Muškarov, Structures presque hermitiennes sur des espaces twistoriels et leurs types, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987) 307 MR910366
26	P A Nagy, Nearly Kähler geometry and Riemannian foliations, Asian J. Math. 6 (2002) 481 MR1946344
27	I Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. U.S.A. 42 (1956) 359 MR0079769
28	I Satake, The Gauss-Bonnet theorem for $V$–manifolds, J. Math. Soc. Japan 9 (1957) 464 MR0095520
29	M Verbitsky, Hyper-Kähler manifolds with torsion, supersymmetry and Hodge theory, Asian J. Math. 6 (2002) 679 MR1958088
30	M Verbitsky, Theorems on the vanishing of cohomology for locally conformally hyper-Kähler manifolds, Tr. Mat. Inst. Steklova 246 (2004) 64 MR2101284
31	M Verbitsky, An intrinsic volume functional on almost complex $6$–manifolds and nearly Kähler geometry, Pacific J. Math. 235 (2008) 323 MR2386227