A. Aazami

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20242026

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math.DG2026

Hodge Splittings and Einstein 4-manifolds

Amir Babak Aazami

On an oriented $4$ -manifold, we study pairs of Riemannian metrics $(g, h)$ for which the curvature tensor of $g$ preserves the Hodge splitting determined by $h$ . This extends the Ei…

math.DG2026

On normal forms of gradient Ricci 4-solitons

Amir Babak Aazami

In this note we analyze the normal form of the operator $R^+ \frac{1}{2} H^$ of a gradient Ricci 4-soliton in Cao & Tran. In particular, we show that the curvature operat…

math.DG2025

On the curvature operator in dimensions $4 n$

Amir Babak Aazami

We study oriented Riemannian $4 n$ -manifolds whose Thorpe $2 n^{th}$ curvature operator $R^_{2 n} : I^^{2 n} ⟶ I^^{2 n}$ , or its Weyl analogue $\hat{W}_{2n}…

math.DG2025

On the Curvature and Topology of Compact Stationary Spacetimes

Amir Babak Aazami

Using the result of Petersen & Wink '21, we find obstructions to the curvature and topology of compact Lorentzian manifolds admitting a unit-length timelike Killing vector field.

math.DG2025

Geometry via Plane wave limits

Amir Babak Aazami

Utilizing the covariant formulation of Penrose's plane wave limit by Blau et~al., we construct for any semi-Riemannian metric $g$ a family of "plane wave limits." These limits are…

math.DG2024

Petrov Types for the Weyl Tensor via the Riemannian-to-Lorentzian Bridge

Amir Babak Aazami

We analyze oriented Riemannian 4-manifolds whose Weyl tensors $W$ satisfy the conformally invariant condition $W (T, \cdot, \cdot, T) = 0$ for some nonzero vector $T$ . While this can b…

Hodge Splittings and Einstein 4-manifolds

On normal forms of gradient Ricci 4-solitons

On the curvature operator in dimensions 4n

On the Curvature and Topology of Compact Stationary Spacetimes

Geometry via Plane wave limits

Petrov Types for the Weyl Tensor via the Riemannian-to-Lorentzian Bridge

On the curvature operator in dimensions $4 n$