The

covariant derivatives of a tensor of order two are also tensors and are represented as

One-way analysis of covariance (ANCOVA), with pretest scores as

covariants, were used when tests for homogeneity of variance dictated that ANCOVA was warranted.

Table 2 Closure Status by Race, District, and Severity of Disability with Education as a

CovariantThus, to the extent that income growth and population growth are not

covariant, the initial condition requires greater lift to keep high-income regions aloft relatively, and therein lies the tendency toward PCPI relative convergence, all else being equal.

The differences in survival were seen across

covariant factors such as stage of disease and performance status.

The year 2015 also marks the 100th anniversary of Einstein's geometric theory of space-time and gravitation, the General Theory of Relativity, since the final formulation of the generally

covariant Einstein's field equations of gravitation in the last quarter of 1915 (during a very tragic and difficult time of World War I).

where A, B, C are three non-zero 1-forms, and [nabla] denotes the operator of

covariant differentiation with respect to the metric g.

The

covariant theory of gravitation (CTG) appeared in 2009 [1], as a consequence of the relativistic generalization of the Lorentz-invariant theory of gravitation (LITG).

His topics include the basics of geometry and relativity, affine connection and

covariant derivative, the geodesic equation and its applications, curvature tensor and Einstein's equation, black holes, and cosmological models and the big bang theory.

The first and the second

covariant derivative of the second fundamental form h are given by

Let [nabla] and R be the

covariant differentiation in [M.

where [DELTA] denotes the operator of

covariant differentiation with respect to the metric tensor g and A, B are nowhere vanishing 1-forms such that g(X, [rho]) = A(X) and g(X, [mu]) = B(X) for all X and [rho], [mu] are called the basic vector fields of the manifold.