normal bundle


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normal bundle

[¦nȯr·məl ¦bən·dəl]
(mathematics)
If A is a manifold and B is a submanifold of A, then the normal bundle of B in A is the set of pairs (x,y), where x is in B, y is a tangent vector to A, and y is orthogonal to B.
References in periodicals archive ?
a foliation on a smooth manifold such that the normal bundle is endowed with a metric whose Lie derivative is zero along leaf directions (see [11]).
Let TM be the tangent bundle of M, TF its integrable subbundle given by F, and Q = TM/TF the corresponding normal bundle of F.
where t[xi], and f[xi], are the tangential and normal components of J[xi], respectively Then f[xi], is an endomorphism of the normal bundle [T.
By the end of the first day we had raised pounds 20,000 and by the end of the weekend we had raised pounds 50,000 and then the postman arrived in the office, not just with the normal bundle of mail, but with sacks of mail.
In this paper, we consider totally real submanifold with constant scalar curvature and flat normal bundle and we use the method of proof which is given in [6] and [9].
Wright had been his normal bundle of energy in an opening spell when the pace of strikers Salaheddine Bassir and Rachid Rokki had caused occasional problems fora ba ck trio marshalled by Aston Villa's Gareth Southgate, and Gascoigne's dilly-dallying on the ball did let Youssef Chippo run menacingly once or twice.
k](j)) denotes the total space of the normal bundle [v.
On the other hand, since the tangent bundle is J-invariant, so are the normal bundle.
N] denotes the normal bundle of N, and the direct sum is orthogonal and compatible with the action of [C.
Namely, by the normal bundle we mean the bundle i[f.
A from M, and replaces it with the projectivization of the normal bundle of A in M in the most natural way possible.
In the case n = 2 the solution to the problem is predicted by the equivalent conjectures of Segre, Harbourne, Gimigliano and Hirschowitz [17, 10, 9, 12], hereafter "SHGH conjecture", that can be formulated in the following way: the divisor D is special if and only if there exists a rational curve C whose normal bundle is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and such that D x C [less than or equal to] -2.