An axisymmetric collapse of non-rotating gravitational waves is numerically investigated in the subcritical regime where no black holes form but where curvature attains a maximum and decreases, following the dispersion of the initial wave packet. We find that near the threshold for black hole formation a curvature invariant with dimensions of length, scales as a power-law with the approximate e...

High resolution growth recording techniques and reverse isotope dilution analysis were used to study the relationship between indole-3-acetic acid (IAA) concentration and curvature of excised bean (Phaseolus vulgaris L. cv Bush Burpee Stringless) first internode sections unilaterally treated with hormone. The maximum rate of curvature occurred rapidly (within 25 minutes) and was proportional to...

We construct some examples of analytic solutions of the low energy (i.e. tree-level) string cosmological effective action. We work with the “minimal” field content (i.e. graviton and dilaton) in the absence of any dilaton potential. Provided the metric is sufficiently inhomogeneous (but still diagonal) we find solutions whose curvature invariants are bounded and everywhere defined in time and s...

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.

in this paper, by modifying cheng-yau$'$s technique to complete hypersurfaces in $s^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [h. li, hypersurfaces with constant scalar curvature in space forms, {em math. ann.} {305} (1996), 665--672].

Let Mn be a Riemannian n-manifold. Denote by S(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature on Mn, respectively. In this paper we prove that every C-totally real submanifolds of a Sasakian space form M̄2m+1(c) satisfies S ≤ ( (n−1)(c+3) 4 + n 2 4 H2)g, where H2 and g are the square mean curvature function and metric tensor on Mn, respectively. The equality holds identically if ...

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

Experiments were performed on a neuro-musculo-mechanical model of a lamprey, to explore the strategies for controlling swimming speed. The muscle component of the model was based on previous experiments on isolated lamprey muscle. The patterns of muscle activation were those found in EMG studies on swimming lampreys. The fluid mechanics were modelled with G.I. Taylor's simplification. Tail beat...