TY - CHAP
T1 - On the Existence of η-Einstein Contact Metric Structures
AU - Wade, Aïssa
AU - Ndiaye, Ameth
AU - Diallo, Abdoul Salam
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - The goal of this paper is two-fold: firstly, we give a necessary and sufficient condition for the existence of a transverse Einstein metric on a given co-oriented contact manifold (M,η). Secondly, we apply this result to obtain important consequences. In particular, we give another proof of a theorem by Boyer and Galicki (Sasakian Geometry. Oxford Mathematical Monographs. Oxford University Press, Oxford (2008). xii+613pp.) on solutions to Goldberg’s conjecture for η-Einstein K-contact manifolds. An example illustrating our construction result is provided.
AB - The goal of this paper is two-fold: firstly, we give a necessary and sufficient condition for the existence of a transverse Einstein metric on a given co-oriented contact manifold (M,η). Secondly, we apply this result to obtain important consequences. In particular, we give another proof of a theorem by Boyer and Galicki (Sasakian Geometry. Oxford Mathematical Monographs. Oxford University Press, Oxford (2008). xii+613pp.) on solutions to Goldberg’s conjecture for η-Einstein K-contact manifolds. An example illustrating our construction result is provided.
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U2 - 10.1007/978-3-031-52681-7_12
DO - 10.1007/978-3-031-52681-7_12
M3 - Chapter
AN - SCOPUS:85195919485
T3 - Trends in Mathematics
SP - 267
EP - 283
BT - Trends in Mathematics
PB - Springer Science and Business Media Deutschland GmbH
ER -