A note on the volume of -Einstein manifolds with skew-torsion
Communications in Mathematics (2021)
- Volume: 29, Issue: 3, page 385-393
- ISSN: 1804-1388
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topChrysikos, Ioannis. "A note on the volume of $\nabla $-Einstein manifolds with skew-torsion." Communications in Mathematics 29.3 (2021): 385-393. <http://eudml.org/doc/298101>.
@article{Chrysikos2021,
abstract = {We study the volume of compact Riemannian manifolds which are Einstein with respect to a metric connection with (parallel) skew-torsion. We provide a result for the sign of the first variation of the volume in terms of the corresponding scalar curvature. This generalizes a result of M. Ville [Vil] related with the first variation of the volume on a compact Einstein manifold.},
author = {Chrysikos, Ioannis},
journal = {Communications in Mathematics},
keywords = {connections with totally skew-symmetric torsion; scalar curvature; $\nabla $-Einstein manifolds; parallel skew-torsion},
language = {eng},
number = {3},
pages = {385-393},
publisher = {University of Ostrava},
title = {A note on the volume of $\nabla $-Einstein manifolds with skew-torsion},
url = {http://eudml.org/doc/298101},
volume = {29},
year = {2021},
}
TY - JOUR
AU - Chrysikos, Ioannis
TI - A note on the volume of $\nabla $-Einstein manifolds with skew-torsion
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 3
SP - 385
EP - 393
AB - We study the volume of compact Riemannian manifolds which are Einstein with respect to a metric connection with (parallel) skew-torsion. We provide a result for the sign of the first variation of the volume in terms of the corresponding scalar curvature. This generalizes a result of M. Ville [Vil] related with the first variation of the volume on a compact Einstein manifold.
LA - eng
KW - connections with totally skew-symmetric torsion; scalar curvature; $\nabla $-Einstein manifolds; parallel skew-torsion
UR - http://eudml.org/doc/298101
ER -
References
top- Agricola, I., Ferreira, A.C., 10.1093/qmath/hat050, Oxford Quart. J., 65, 2014, 717-741, (2014) MR3261964DOI10.1093/qmath/hat050
- Agricola, I., Friedrich, Th., 10.1007/s00208-003-0507-9, Math. Ann., 328, 2004, 711-748, (2004) Zbl1055.53031MR2047649DOI10.1007/s00208-003-0507-9
- Agricola, I., Becker-Bender, J., Kim, H., 10.1016/j.aim.2013.05.001, Adv. Math., 243, 2013, 296-329, (2013) MR3062748DOI10.1016/j.aim.2013.05.001
- Ammann, B., Bär, C., The Einstein-Hilbert action as a spectral action, Noncommutative Geometry and the Standard Model of Elementary Particle Physics, 2002, 75-108, (2002) MR1998531
- Besse, A.L., Einstein manifolds, 1987, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, (1987) Zbl0613.53001
- Chrysikos, I., Invariant connections with skew-torsion and -Einstein manifolds, J. Lie Theory, 26, 2016, 11-48, (2016) MR3384980
- Chrysikos, I., 10.1007/s10455-015-9483-z, Ann. Glob. Anal. Geom., 49, 2016, 105-141, (2016) MR3464216DOI10.1007/s10455-015-9483-z
- Chrysikos, I., 10.1007/s00006-017-0810-2, Adv. Appl. Clifford Algebras, 27, 2017, 3097-3127, (2017) MR3718180DOI10.1007/s00006-017-0810-2
- Chrysikos, I., Gustad, C. O'Cadiz, Winther, H., 10.1016/j.geomphys.2018.10.012, J. Geom. Phys., 138, 2019, 257-284, (2019) MR3945042DOI10.1016/j.geomphys.2018.10.012
- Draper, C.A., Garvin, A., Palomo, F.J., 10.1007/s10455-015-9489-6, Ann. Glob. Anal. Geom., 49, 2016, 213-251, (2016) MR3485984DOI10.1007/s10455-015-9489-6
- Draper, C.A., Garvin, A., Palomo, F.J., 10.1016/j.geomphys.2018.08.006, J. Geom. Phys., 134, 2017, 133-141, (2017) MR3886931DOI10.1016/j.geomphys.2018.08.006
- Friedrich, Th., Ivanov, S., Parallel spinors and connections with skew-symmetric torsion in string theory, Asian J. Math., 6, 1962, 64-94, (1962)
- Friedrich, Th., Kim, E.C., 10.1016/S0393-0440(99)00043-1, J. Geom. Phys., 33, 2000, 128-172, (2000) DOI10.1016/S0393-0440(99)00043-1
- Kühnel, W., Differential Geometry, Curves--Surfaces--Manifolds, 2002, Amer. Math. Soc. Student Math. Library, (2002) MR1882174
- Ville, M., Sur le volume des variétés riemanniennes pincées, Bulletin de la S. M. F., 115, 1987, 127-139, (1987)
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