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71.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
72.
Zhen-han Tu 《Proceedings of the American Mathematical Society》1999,127(4):1039-1049
By applying the heuristic principle in several complex variables obtained by Aladro and Krantz, we shall prove some normality criteria for families of holomorphic mappings of several complex variables into , the complex N-dimensional projective space, related to Green's and Nochka's Picard type theorems. The equivalence of normality to being uniformly Montel at a point will be obtained. Some examples will be given to complement our theory in this paper.
73.
J M Landsberg 《Compositio Mathematica》1999,118(2):189-201
Let XP be a variety (respectively an open subset of an analytic submanifold) and let xX be a point where all integer valued differential invariants are locally constant. We show that if the projective second fundamental form of X at x is isomorphic to the second fundamental form of a point of a Segre P× P, n,m2, a Grassmaniann G(2,n+2), n4, or the Cayley plane OP2, then X is the corresponding homogeneous variety (resp. an open subset of the corresponding homogeneous variety). The case of the Segre P2×P2 had been conjectured by Griffiths and Harris in [GH]. If the projective second fundamental form of X at x is isomorphic to the second fundamental form of a point of a Veronese v2(P) and the Fubini cubic form of X at x is zero, then X=v2 (P) (resp. an open subset of v2(P)). All these results are valid in the real or complex analytic categories and locally in the C category if one assumes the hypotheses hold in a neighborhood of any point x. As a byproduct, we show that the systems of quadrics I2(P P) S2C, I2(P1× P) S2C and I2(S5) S2C16 are stable in the sense that if A S* is an analytic family such that for t0,AA, then A0A. We also make some observations related to the Fulton–:Hansen connectedness theorem. 相似文献
74.
Alexander Kreuzer 《Geometriae Dedicata》1999,76(1):43-52
This note deals with the following question: How many planes of a linear space (P, $\mathfrak{L}$ ) must be known as projective planes to ensure that (P, $\mathfrak{L}$ ) is a projective space? The following answer is given: If for any subset M of a linear space (P, $\mathfrak{L}$ ) the restriction (M, $\mathfrak{L}$ )(M)) is locally complete, and if for every plane E of (M, $\mathfrak{L}$ (M)) the plane $\bar E$ generated by E is a projective plane, then (P, $\mathfrak{L}$ ) is a projective space (cf. 5.6). Or more generally: If for any subset M of P the restriction (M, $\mathfrak{L}$ (M)) is locally complete, and if for any two distinct coplanar lines G1, G2 ∈ $\mathfrak{L}$ (M) the lines $\bar G_1 ,\bar G_2 \varepsilon \mathfrak{L}$ generated by G1, G2 have a nonempty intersection and $\overline {G_1 \cup {\text{ }}G_2 }$ satisfies the exchange condition, then (P, $\mathfrak{L}$ ) is a generalized projective space. 相似文献
75.
Tatsuya Maruta 《Geometriae Dedicata》1999,74(3):305-311
Any {f,r- 2+s; r,q}-minihyper includes a hyperplane in PG(r, q) if fr-1 + s 1 + q – 1 for 1 s q – 1, q 3, r 4, where i = (qi + 1 – 1)/ (q – 1 ). A lower bound on f for which an {f, r – 2 + 1; r, q}-minihyper with q 3, r 4 exists is also given. As an application to coding theory, we show the nonexistence of [ n, k, n + 1 – qk – 2 ]q codes for k 5, q 3 for qk – 1 – 2q – 1 < n qk – 1 – q – 1 when k > q –
q - \sqrt q + 2$$
" align="middle" border="0">
and for
when
, which is a generalization of [18, Them. 2.4]. 相似文献
76.
Hauke Klein 《Geometriae Dedicata》1999,77(3):271-277
We consider a four-dimensional compact projective plane
whose collineation group is six-dimensional and solvable with a nilradical N isomorphic to Nil×R, where Nil denotes the three-dimensional, simply connected, non-Abelian, nilpotent Lie group. We assume that fixes a flag p W, acts transitively on
and fixes no point in the set W\p. Under these conditions, we will prove that either contains a three-dimensional group of elations or acts doubly transitively on
. 相似文献
77.
2-HarmonicTotallyRealSubmanifoldsinaComplex Projective SpaceSunHongan(孙弘安)(SouthernInstituteofMetallurgy)Abstract:Inthispaper... 相似文献
78.
P. Delorme 《Journal of Functional Analysis》2004,217(2):314-346
We introduce a filtration of a -module of some space of functions on a reductive symmetric space G/H, and compute the associated grading as a direct sum of induced representations. As an application of this result to the reductive groups viewed as symmetric spaces, we are able to realize any Harish-Chandra module as a subquotient of a direct sum of induced representations from parabolic subgroups, the inducing representations being trivial on the unipotent radical. 相似文献
79.
The analysis of the Fourier Transform Mechanical Spectroscopy (FTMS) method in application to measuring viscoelastic properties of a material in a linear viscoelastic domain shows that sensitivity of the method at higher harmonics strongly depends on the form of the input signal. Then the problem of the choice of the optimal signal is discussed. It is shown that the function f(t)=(sint)/t provides the best form of the input signal basing on the requirement to hold equal amplitudes of all higher harmonics. The comparison of data obtained by the FTMS method and viscoelastic properties measured in harmonic oscillations demonstrates that both methods give adequate results.The application of the FTMS method with the input signal of the optimal form for measuring linear viscoelastic properties of a material saves time of an experiment (up to 3–4 times) and might be specially interesting for analysis of unstable (rheokinetic) materials, in particular, curing oligomers, because the time evolution of different relaxation modes can proceed in different manner. 相似文献
80.
Let G be a locally compact group, and let L1 (G) be the Banachalgebra which is the group algebra of G. We consider a varietyof Banach left L1 (G)-modules over L1 (G), and seek to determineconditions on G that determine when these modules are eitherprojective or injective or flat in the category. The answerstypically involve G being compact or discrete or amenable. Forexample, in the case where G is discrete and 1 < p < ,we find that the module p (G) is injective whenever G is amenable,and that, if it is amenable, then G is pseudo-amenable,a property very close to that of amenability. 2000 MathematicsSubject Classification 46H25, 43A20. 相似文献