Curvature of almost quaternion-Hermitian manifolds

TY - JOUR

T1 - Curvature of almost quaternion-Hermitian manifolds

AU - Cabrera, Francisco Martn

AU - Swann, Andrew

PY - 2010/1/1

Y1 - 2010/1/1

N2 - We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n) Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion and its covariant derivative and determine relations between the decompositions of ⊗ , and R. We pay particular attention to the behaviour of the Ricci curvature and the q-Ricci curvature.

AB - We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n) Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion and its covariant derivative and determine relations between the decompositions of ⊗ , and R. We pay particular attention to the behaviour of the Ricci curvature and the q-Ricci curvature.

UR - http://www.scopus.com/inward/record.url?scp=77950229817&partnerID=8YFLogxK

U2 - 10.1515/FORUM.2010.002

DO - 10.1515/FORUM.2010.002

M3 - Journal article

AN - SCOPUS:77950229817

SN - 0933-7741

VL - 22

SP - 21

EP - 52

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 1

ER -