The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are found for the Lagrangians with quadratic dependence on curvatures, for the Lagrangians, proportional to an arbitrary curvature, and for the Lagrangians, linear o...

In a study of Riemannian manifolds admitting conformal transformation, the Riemannian and Ricci curvatures play an important role for characterizations and classify such a manifold. In this note, we summarize known results about Riemannian manifold admitting conformal transformations and related topics.

I discuss an old result of John Milnor stating roughly that if a closed curve in space is not too curved then it cannot be knotted. CONTENTS 1. The total curvature of a polygonal curve 1 2. A probabilistic interpretation of the total curvature 2 3. The total curvature of a smooth closed curve 4 4. Total curvature and knotting 6 References 7 1. THE TOTAL CURVATURE OF A POLYGONAL CURVE An (orient...

[1] Nearly complete coverage of shipboard multibeam bathymetry data at the right‐stepping Menard and Pitman Fracture Zones allowed us to map abyssal hill deviations along their traces. In this study we distinguish between (1) J‐shaped curvatures at their origin, where modeling is addressing primary volcanism and faulting following a curved zone, and (2) straight abyssal hills getting bent in an...

Purpose. The aim of the study was an assessment of posture in women who regularly perform aerobic exercise. Methods. The study group consisted of 50 women actively participating in aerobics classes (mean: age 28.64 ± 5.3 years, body mass 59.83 ± 6.7 kg, height 167.75 ± 4.9 cm, bMI 21.24 ± 3.6 m/kg) and a control group of 50 women not involved in any regular physical activity (mean: age 28.55 ± ...

The primary cilium is an outward projecting antenna-like organelle with an important role in bone mechanotransduction. The capacity to sense mechanical stimuli can affect important cellular and molecular aspects of bone tissue. Idiopathic scoliosis (IS) is a complex pediatric disease of unknown cause, defined by abnormal spinal curvatures. We demonstrate significant elongation of primary cilia ...