Sentence examples for fundamental form is from inspiring English sources

Thus, (c ne 0), and the second fundamental form is non-zero at each point on the surface.

There was surely some bickering here, as there was between AC and DC when prototyping electrical devices, but one fundamental form is almost always selected, and for the car it was four wheels, front engine, and internal combustion.

The second fundamental form is defined by begin{aligned} h(e_i,e_j) = langle D_{e_i} nu,e_j rangle, end{aligned}where ({e_1,e_2}) is an orthonormal basis of tangent vectors to (Sigma ).

The proof given in [11] for these inequalities is based on an optimization procedure by showing that a quadratic polynomial in the components of the second fundamental form is parabolic.

These inequalities were recently obtained in Lee and Vîlcu (Taiwan. J. Math. 19(3):691-702015015) using an optimization procedure by showing that a quadratic polynomial in the components of the second fundamental form is parabolic.

In order to exploit the latter condition, we make use of the following result due to Lawson: (Lawson [37]) An immersed minimal surface in (S^3) of genus (1) has no umbilic points; in other words, the second fundamental form is non-zero at each point on the surface.

The second fundamental form being begin{aligned} II_0 vec {X},vec {Y})=(dn_0 vec {X}),vec {Y})hbox { for }vec {X},vec {Y}in T_0partial Omega, end{aligned}where (dn_0) is the differential of the outward normal vector at 0 and ((cdot,cdot )) is the Euclidean scalar product.

The second fundamental forms are related by their shape operators, begin{aligned}& B^{N} X,Y =gbigl(A^_{xi}X,Ybigr),qquad overline{g}bigl(A^_{xi}X,Nbigr)=0, end{aligned} (18) begin{aligned}& C^{N} X,PY =g(A_{N}X,PY), qquadoverline{g}(A_{N}Y,N =0,quad forall X,YinGamma(TM).

The fundamental bilateral body form is a tube with a hollow gut cavity running from the mouth to the anus, and a nerve cord with an enlargement (a ganglion) for each body segment, with an especially large ganglion at the front, called the brain.

In other cases, it is considered that the ordinary simple spiral, and the ordinary bijugate, are fundamental forms --- that is, forms with either of which a cone may commence without the intervention of another.

Let p ∈ M and Π = sp { e i, e j } be a two-dimensional non-degenerate plane of T p M. The number K i j = g ( R ( e j, e i ) e i, e j ) g ( e i, e i ) g ( e j, e j ) − g ( e i, e j ) 2. is called the sectional curvature at p ∈ M. Since the screen second fundamental form C is not symmetric, the sectional curvature K i j of a lightlike submanifold is not symmetric, that is, K i j ≠ K j i.