SMAS-flap transposition in Lower Face-lift

The superficial musculoaponeurotic system is of fundamental importance in facial anatomy. One of its primary functions is to harmoniously integrate the facial mimic muscles by coordinating their movements with each other. The continuity of the superficial musculoaponeurotic system with the platysma also creates an effective unitary connection with the mandibular and cervical areas. For these areas, where the signs of aging are first shown with soft tissue ptosis and cervical bands, we propose our lower face-lift technique with SMAS-flap transposition. This technique is not characterized by the section of the aponeurosis at the earlobe or lower level and by its rotation, but it is characterized by an higher SMAS section at tragus level with transposition of the mobilized pre-parotid and platysma aponeurosis to the high mastoid area. This manoeuvrer allows us for an effective platysma extension-lift and for his secure fixation to the upper mastoid area, resulting in greater stability and duration of the treatment.

Twisted dirac operators and Kastler-Kalau-Walze theorems for six-dimensional manifolds with boundary

In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.

Quaternion-Kähler manifolds near maximal fixed point sets of $$S^1$$-symmetries

Using quaternionic Feix–Kaledin construction, we provide a local classification of quaternion-Kähler metrics with a rotating $$S^1$$S1-symmetry with the fixed point set submanifold S of maximal possible dimension. For any real-analytic Kähler manifold S equipped with a line bundle with a real-analytic unitary connection with curvature proportional to the Kähler form, we explicitly construct a holomorphic contact distribution on the twistor space obtained by the quaternionic Feix–Kaledin construction from these data. Conversely, we show that quaternion-Kähler metrics with a rotating $$S^1$$S1-symmetry induce on the fixed point set of maximal dimension a Kähler metric together with a unitary connection on a holomorphic line bundle with curvature proportional to the Kähler form and the two constructions are inverse to each other. Moreover, we study the case when S is compact, showing that in this case the quaternion-Kähler geometry is determined by the Kähler metric on the fixed point set (of maximal possible dimension) and by the contact line bundle along the corresponding submanifold on the twistor space. Finally, we relate the results to the c-map construction showing that the family of quaternion-Kähler manifolds obtained from a fixed Kähler metric on S by varying the line bundle and the hyperkähler manifold obtained by hyperkähler Feix–Kaledin construction from S are related by hyperkähler/quaternion-Kähler correspondence.

The tensor product of supersymmetric N = (1,1) spectral data

We define the notion of tensor product of supersymmetric [Formula: see text] spectral data in the context of supersymmetric quantum theory and noncommutative geometry. We explain in which sense our definition is canonical and also establish its compatibility with the tensor product of [Formula: see text] spectral data defined earlier by Connes. As an application, we show that the unitary connections on the individual [Formula: see text] spectral data give rise to a unitary connection on the product [Formula: see text] spectral data.