Tohoku Mathematical Journal
2024
June
SECOND SERIES VOL. 76, NO. 2

Tohoku Math. J.
76 (2024), 255-292

Title THE H/Q-CORRESPONDENCE AND A GENERALIZATION OF THE SUPERGRAVITY C-MAP

Author Vicente Cortés and Kazuyuki Hasegawa

(Received August 1, 2022, revised October 27, 2022)
Abstract. Given a hypercomplex manifold with a rotating vector field (and additional data), we construct a conical hypercomplex manifold. As a consequence, we associate a quaternionic manifold to a hypercomplex manifold of the same dimension with a rotating vector field. This is a generalization of the HK/QK-correspondence. As an application, we show that a quaternionic manifold can be associated to a conical special complex manifold of half its dimension. Furthermore, a projective special complex manifold (with a canonical c-projective structure) associates with a quaternionic manifold. The latter is a generalization of the supergravity c-map. We do also show that the tangent bundle of any special complex manifold carries a canonical Ricci-flat hypercomplex structure, thereby generalizing the rigid c-map.

Mathematics Subject Classification. Primary 53C10; Secondary 53C56, 53C26.
Key words and phrases. Conical hypercomplex manifold, H/Q--correspondence, generalized supergravity c-map.

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