On totally real bisectional curvature

We obtain some basic results for Riemannian curvature tensor of (ε)-Sasakian manifolds and then establish equivalent relations amongφ-sectional curvature, totally real sectional curvature, and totally real bisectional curvature for (ε)-Sasakian manifolds.

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THE DEGREE OF HOLOMORPHIC APPROXIMATION ON A TOTALLY REAL SET

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972708001226 ◽

2009 ◽

Vol 79 (1) ◽

pp. 171-176

Author(s):

SAID ASSERDA

Keyword(s):

Compact Support ◽

Infinite Order ◽

Holomorphic Functions ◽

Degree Of Approximation ◽

Gevrey Class ◽

Bisectional Curvature ◽

Bounded Geometry ◽

Holomorphic Bisectional Curvature ◽

Open Set ◽

Totally Real

AbstractLet E be a totally real set on a Stein open set Ω on a complete noncompact Kähler manifold (M,g) with nonnegative holomorphic bisectional curvature such that (Ω,g) has bounded geometry at E. Then every function f in a Cp class with compact support on Ω and $\overline \partial $-flat on E up to order p−1,p≥2 (respectively, in a Gevrey class of order s>1, with compact support on Ω and $\overline \partial $-flat on E up to infinite order) can be approximated on compacts subsets of E by holomorphic functions fk on Ω with degree of approximation equal k−p/2 (respectively, exp (−c(s)k1/2(s−1)) ).

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Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽

10.2298/fil1720449a ◽

2017 ◽

Vol 31 (20) ◽

pp. 6449-6459 ◽

Cited By ~ 2

Author(s):

Akram Ali ◽

Siraj Uddin ◽

Wan Othman ◽

Cenap Ozel

Keyword(s):

Sectional Curvature ◽

Mean Curvature ◽

Warped Product ◽

Warped Products ◽

Equality Case ◽

Cosymplectic Manifolds ◽

Almost Cosymplectic Manifold ◽

Locally Conformal ◽

Totally Real ◽

Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

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Finite slope triple product p-adic L-functions over totally real number fields

Journal of Number Theory ◽

10.1016/j.jnt.2020.11.013 ◽

2020 ◽

Author(s):

Santiago Molina

Keyword(s):

Real Number ◽

Number Fields ◽

Triple Product ◽

Totally Real ◽

Finite Slope

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The determination of units in totally real cubic fields

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100034617 ◽

1960 ◽

Vol 56 (4) ◽

pp. 318-321 ◽

Cited By ~ 12

Author(s):

H. J. Godwin

Keyword(s):

Trial And Error ◽

Integral Lattice ◽

Cubic Field ◽

Cubic Fields ◽

Trial And Error Method ◽

Totally Real ◽

Rational Integral ◽

Fundamental Units ◽

Error Method

The determination of a pair of fundamental units in a totally real cubic field involves two operations—finding a pair of independent units (i.e. such that neither is a power of the other) and from these a pair of fundamental units (i.e. a pair ε1; ε2 such that every unit of the field is of the form with rational integral m, n). The first operation may be accomplished by exploring regions of the integral lattice in which two conjugates are small or else by factorizing small primes and comparing different factorizations—a trial-and-error method, but often a quick one. The second operation is accomplished by obtaining inequalities which must be satisfied by a fundamental unit and its conjugates and finding whether or not a unit exists satisfying these inequalities. Recently Billevitch ((1), (2)) has given a method, of the nature of an extension of the first method mentioned above, which involves less work on the second operation but no less on the first.

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