The purpose of this paper is to consider q-Euler numbers and polynomials which are q-extensions of ordinary Euler numbers and polynomials by the computations of the p-adic q-integrals due to T. Kim, cf. [1,3,6,12], and to derive the "complete sums for q-Euler polynomials" which are evaluated by using multivariate p-adic q-integrals. These sums help us to study the relationships between p-adic q-integrals and nonarchimedean combinatorial analysis.
Abstract. We shall give some curvature conditions for the unit tangent sphere bundle of an n(≥ 4)-dimensional Riemannian manifold to be Hcontact. Furthermore, we provide an example illustrating Main Theorem.
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