Normal complex contact metric manifolds admitting a semi symmetric metric connection

In this paper, we study on normal complex contact metric manifold admitting a semi symmetric metric connection. We obtain curvature properties of a normal complex contact metric manifold admitting a semi symmetric metric connection. We also prove that this type of manifold is not conformal flat, concircular flat, and conharmonic flat. Finally, we examine complex Heisenberg group with the semi symmetric metric connection.

Submanifolds in Normal Complex Contact Manifolds

In the present article we initiate the study of submanifolds in normal complex contact metric manifolds. We define invariant and anti-invariant ( C C -totally real) submanifolds in such manifolds and start the study of their basic properties. Also, we establish the Chen first inequality and Chen inequality for the invariant δ ( 2 , 2 ) for C C -totally real submanifolds in a normal complex contact space form and characterize the equality cases. We also prove the minimality of C C -totally real submanifolds of maximum dimension satisfying the equalities.

H-curvature tensors on IK-normal complex contact metric manifolds

IK-normal complex contact metric manifolds have some important properties. There are several applications of this kind of contact manifolds in theoretical physics. In this paper, we studied on [Formula: see text]-curvature tensors for IK-normal complex contact metric manifolds. We have shown that there is no IK-normal complex contact metric manifold with constant sectional curvature and an IK-normal complex contact metric manifold is not Ricci semi-symmetric.

On equivariant Serre problem for principal bundles

Let [Formula: see text] be a [Formula: see text]-equivariant algebraic principal [Formula: see text]-bundle over a normal complex affine variety [Formula: see text] equipped with an action of [Formula: see text], where [Formula: see text] and [Formula: see text] are complex linear algebraic groups. Suppose [Formula: see text] is contractible as a topological [Formula: see text]-space with a dense orbit, and [Formula: see text] is a [Formula: see text]-fixed point. We show that if [Formula: see text] is reductive, then [Formula: see text] admits a [Formula: see text]-equivariant isomorphism with the product principal [Formula: see text]-bundle [Formula: see text], where [Formula: see text] is a homomorphism between algebraic groups. As a consequence, any torus equivariant principal [Formula: see text]-bundle over an affine toric variety is equivariantly trivial. This leads to a classification of torus equivariant principal [Formula: see text]-bundles over any complex toric variety, generalizing the main result of [A classification of equivariant principal bundles over nonsingular toric varieties, Internat. J. Math. 27(14) (2016)].

Conformal, concircular, quasi-conformal and conharmonic flatness on normal complex contact metric manifolds

Conformal, concircular, quasi-conformal and conharmonic curvature tensors play an important role in Riemannian geometry. In this paper, we study on normal complex contact metric manifolds under flatness conditions of these tensors.

On the fundamental groups of normal varieties

We show that the fundamental groups of normal complex algebraic varieties share many properties of the fundamental groups of smooth varieties. The jump loci of rank one local systems on a normal variety are related to the jump loci of a resolution and of a smoothing of this variety.

Threefolds in ℙ6 of degree 12

Linearly normal complex projective threefolds of degree 12, embedded in ℙ

Mechanisms of Innovation in the Space and Defense Sector

Despite a rich legacy of space sector technological achievements, agencies are increasingly being criticized for their inability to deliver on their innovative promises. Although the phenomenon of innovation has received substantial attention across multiple disciplines, it has largely focused on relatively simple products in nearly competitive markets, making its applicability to the space system context suspect. This paper reviews the economic, political science/strategic, business and operational literatures most relevant to complex product innovation in government markets. It categorizes their insights in terms of the sources of innovation as – external political-level leadership, internal bureaucratic politics, structure of the system, new technologies and user innovations – to illustrate the overlap and gaps among the disciplinary insights. It argues that past studies have over emphasized innovations that were generated by idiosyncratic events and have not adequately addressed the architectural dimension of complex product innovation. If useful prescriptions are to be developed, the process of normal complex product innovation in monopsony markets must be examined as a whole. To this end, the paper suggests several priorities for future work.