COMPATIBILITY BETWEEN NON-KÄHLER STRUCTURES ON COMPLEX (NIL)MANIFOLDS
2
Institute of Mathematics, “Simion Stoilow” of the Romanian Academy, Bucharest, Romania
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Publication type: Journal Article
Publication date: 2022-06-02
scimago Q2
SJR: 0.720
CiteScore: 1.6
Impact factor: —
ISSN: 10834362, 1531586X
Algebra and Number Theory
Geometry and Topology
Abstract
We study the interplay between the following types of special non-Kähler Hermitian metrics on compact complex manifolds (locally conformally Kähler, k-Gauduchon, balanced, and locally conformally balanced) and prove that a locally conformally Kähler compact nilmanifold carrying a balanced or a left-invariant k-Gauduchon metric is necessarily a torus. Combined with the main result in [FV16], this leads to the fact that a compact complex 2-step nilmanifold endowed with whichever two of the following types of metrics—balanced, pluriclosed and locally conformally Kähler—is a torus. Moreover, we construct a family of compact nilmanifolds in any dimension carrying both balanced and locally conformally balanced metrics and finally we show a compact complex nilmanifold does not support a left-invariant locally conformally hyper-Kähler structure.
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6
Total citations:
6
Citations from 2024:
4
(66.67%)
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GOST
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Ornea L. et al. COMPATIBILITY BETWEEN NON-KÄHLER STRUCTURES ON COMPLEX (NIL)MANIFOLDS // Transformation Groups. 2022.
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Ornea L., Otiman A. I., Stanciu M. COMPATIBILITY BETWEEN NON-KÄHLER STRUCTURES ON COMPLEX (NIL)MANIFOLDS // Transformation Groups. 2022.
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RIS
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TY - JOUR
DO - 10.1007/s00031-022-09729-5
UR - https://doi.org/10.1007/s00031-022-09729-5
TI - COMPATIBILITY BETWEEN NON-KÄHLER STRUCTURES ON COMPLEX (NIL)MANIFOLDS
T2 - Transformation Groups
AU - Ornea, L
AU - Otiman, A I
AU - Stanciu, M.
PY - 2022
DA - 2022/06/02
PB - Springer Nature
SN - 1083-4362
SN - 1531-586X
ER -
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BibTex (up to 50 authors)
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@article{2022_Ornea,
author = {L Ornea and A I Otiman and M. Stanciu},
title = {COMPATIBILITY BETWEEN NON-KÄHLER STRUCTURES ON COMPLEX (NIL)MANIFOLDS},
journal = {Transformation Groups},
year = {2022},
publisher = {Springer Nature},
month = {jun},
url = {https://doi.org/10.1007/s00031-022-09729-5},
doi = {10.1007/s00031-022-09729-5}
}